diff --git a/tests/integration/data_processing/test_data_processor.py b/tests/integration/data_processing/test_data_processor.py
index 65f865d2f..bb87029b4 100644
--- a/tests/integration/data_processing/test_data_processor.py
+++ b/tests/integration/data_processing/test_data_processor.py
@@ -53,7 +53,7 @@ def test_with_anonymized_columns(self):
         data, metadata = download_demo('single_table', 'adult')
 
         # Add anonymized field
-        metadata.update_column('adult', 'occupation', sdtype='job', pii=True)
+        metadata.update_column('occupation', 'adult', sdtype='job', pii=True)
 
         # Instance ``DataProcessor``
         dp = DataProcessor(metadata._convert_to_single_table())
@@ -101,11 +101,11 @@ def test_with_anonymized_columns_and_primary_key(self):
         data, metadata = download_demo('single_table', 'adult')
 
         # Add anonymized field
-        metadata.update_column('adult', 'occupation', sdtype='job', pii=True)
+        metadata.update_column('occupation', 'adult', sdtype='job', pii=True)
 
         # Add primary key field
-        metadata.add_column('adult', 'id', sdtype='id', regex_format='ID_\\d{4}[0-9]')
-        metadata.set_primary_key('adult', 'id')
+        metadata.add_column('id', 'adult', sdtype='id', regex_format='ID_\\d{4}[0-9]')
+        metadata.set_primary_key('id', 'adult')
 
         # Add id
         size = len(data)
@@ -159,8 +159,8 @@ def test_with_primary_key_numerical(self):
         adult_metadata = Metadata.detect_from_dataframes({'adult': data})
 
         # Add primary key field
-        adult_metadata.add_column('adult', 'id', sdtype='id')
-        adult_metadata.set_primary_key('adult', 'id')
+        adult_metadata.add_column('id', 'adult', sdtype='id')
+        adult_metadata.set_primary_key('id', 'adult')
 
         # Add id
         size = len(data)
@@ -198,13 +198,13 @@ def test_with_alternate_keys(self):
         adult_metadata = Metadata.detect_from_dataframes({'adult': data})
 
         # Add primary key field
-        adult_metadata.add_column('adult', 'id', sdtype='id')
-        adult_metadata.set_primary_key('adult', 'id')
+        adult_metadata.add_column('id', 'adult', sdtype='id')
+        adult_metadata.set_primary_key('id', 'adult')
 
-        adult_metadata.add_column('adult', 'secondary_id', sdtype='id')
-        adult_metadata.update_column('adult', 'fnlwgt', sdtype='id', regex_format='ID_\\d{4}[0-9]')
+        adult_metadata.add_column('secondary_id', 'adult', sdtype='id')
+        adult_metadata.update_column('fnlwgt', 'adult', sdtype='id', regex_format='ID_\\d{4}[0-9]')
 
-        adult_metadata.add_alternate_keys('adult', ['secondary_id', 'fnlwgt'])
+        adult_metadata.add_alternate_keys(['secondary_id', 'fnlwgt'], 'adult')
 
         # Add id
         size = len(data)
@@ -345,7 +345,7 @@ def test_localized_anonymized_columns(self):
         """Test data processor uses the default locale for anonymized columns."""
         # Setup
         data, metadata = download_demo('single_table', 'adult')
-        metadata.update_column('adult', 'occupation', sdtype='job', pii=True)
+        metadata.update_column('occupation', 'adult', sdtype='job', pii=True)
 
         dp = DataProcessor(metadata._convert_to_single_table(), locales=['en_CA', 'fr_CA'])
 
diff --git a/tests/integration/evaluation/test_single_table.py b/tests/integration/evaluation/test_single_table.py
index 8b3cf23fa..d943b02d3 100644
--- a/tests/integration/evaluation/test_single_table.py
+++ b/tests/integration/evaluation/test_single_table.py
@@ -12,7 +12,7 @@ def test_evaluation():
     data = pd.DataFrame({'col': [1, 2, 3]})
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'col', sdtype='numerical')
+    metadata.add_column('col', 'table', sdtype='numerical')
     synthesizer = GaussianCopulaSynthesizer(metadata, default_distribution='truncnorm')
 
     # Run and Assert
diff --git a/tests/integration/metadata/test_metadata.py b/tests/integration/metadata/test_metadata.py
index 5d460e1c9..fd5909b24 100644
--- a/tests/integration/metadata/test_metadata.py
+++ b/tests/integration/metadata/test_metadata.py
@@ -419,54 +419,46 @@ def test_any_metadata_update_single_table(method, args, kwargs):
     metadata.update_column(
         table_name='fake_hotel_guests', column_name='billing_address', sdtype='street_address'
     )
-    metadata_kwargs = deepcopy(metadata)
-    metadata_args = deepcopy(metadata)
-    metadata_kwargs_with_table_name = deepcopy(metadata)
-    metadata_args_with_table_name = deepcopy(metadata)
+    parameter = [kwargs[arg] for arg in args]
+    remaining_kwargs = {key: value for key, value in kwargs.items() if key not in args}
+    metadata_before = deepcopy(metadata).to_dict()
 
     # Run
-    result = getattr(metadata_kwargs, method)(**kwargs)
-    getattr(metadata_kwargs_with_table_name, method)(table_name='fake_hotel_guests', **kwargs)
-    arg_values = [kwargs[arg] for arg in args]
-    extra_param = {key: value for key, value in kwargs.items() if key not in args}
-    getattr(metadata_args, method)(*arg_values, **extra_param)
-    getattr(metadata_args_with_table_name, method)('fake_hotel_guests', *arg_values, **extra_param)
+    result = getattr(metadata, method)(*parameter, **remaining_kwargs)
 
     # Assert
-    expected_dict = metadata_kwargs.to_dict()
+    expected_dict = metadata.to_dict()
     if method != 'get_column_names':
-        assert expected_dict != metadata.to_dict()
+        assert expected_dict != metadata_before
     else:
         assert result == ['checkin_date', 'checkout_date']
 
-    other_metadata = [metadata_args, metadata_kwargs_with_table_name, metadata_args_with_table_name]
-    for metadata_obj in other_metadata:
-        assert expected_dict == metadata_obj.to_dict()
-
 
 @pytest.mark.parametrize('method, args, kwargs', params)
 def test_any_metadata_update_multi_table(method, args, kwargs):
     """Test that any method that updates metadata works for multi-table case."""
     # Setup
-    args.insert(0, 'table_name')
-    kwargs['table_name'] = 'guests'
     _, metadata = download_demo('multi_table', 'fake_hotels')
     metadata.update_column(
         table_name='guests', column_name='billing_address', sdtype='street_address'
     )
-    metadata_kwargs = deepcopy(metadata)
-    metadata_args = deepcopy(metadata)
+    parameter = [kwargs[arg] for arg in args]
+    remaining_kwargs = {key: value for key, value in kwargs.items() if key not in args}
+    metadata_before = deepcopy(metadata).to_dict()
+    expected_error = re.escape(
+        'Metadata contains more than one table, please specify the `table_name`.'
+    )
 
     # Run
-    result = getattr(metadata_kwargs, method)(**kwargs)
-    arg_values = [kwargs[arg] for arg in args]
-    extra_param = {key: value for key, value in kwargs.items() if key not in args}
-    getattr(metadata_args, method)(*arg_values, **extra_param)
+    with pytest.raises(ValueError, match=expected_error):
+        getattr(metadata, method)(*parameter, **remaining_kwargs)
+
+    parameter.append('guests')
+    result = getattr(metadata, method)(*parameter, **remaining_kwargs)
 
     # Assert
-    expected_dict = metadata_kwargs.to_dict()
-    assert expected_dict == metadata_args.to_dict()
+    expected_dict = metadata.to_dict()
     if method != 'get_column_names':
-        assert expected_dict != metadata.to_dict()
+        assert expected_dict != metadata_before
     else:
         assert result == ['checkin_date', 'checkout_date']
diff --git a/tests/integration/metadata/test_multi_table.py b/tests/integration/metadata/test_multi_table.py
index 1384eaf74..23e16de42 100644
--- a/tests/integration/metadata/test_multi_table.py
+++ b/tests/integration/metadata/test_multi_table.py
@@ -34,11 +34,11 @@ def _validate_sdtypes(cls, columns_to_sdtypes):
 
     mock_rdt_transformers.address.RandomLocationGenerator = RandomLocationGeneratorMock
     _, instance = download_demo('multi_table', 'fake_hotels')
-    instance.update_column('hotels', 'city', sdtype='city')
-    instance.update_column('hotels', 'state', sdtype='state')
+    instance.update_column('city', 'hotels', sdtype='city')
+    instance.update_column('state', 'hotels', sdtype='state')
 
     # Run
-    instance.add_column_relationship('hotels', 'address', ['city', 'state'])
+    instance.add_column_relationship('address', ['city', 'state'], 'hotels')
 
     # Assert
     instance.validate()
@@ -303,9 +303,9 @@ def test_get_table_metadata():
     """Test the ``get_table_metadata`` method."""
     # Setup
     metadata = get_multi_table_metadata()
-    metadata.add_column('nesreca', 'latitude', sdtype='latitude')
-    metadata.add_column('nesreca', 'longitude', sdtype='longitude')
-    metadata.add_column_relationship('nesreca', 'gps', ['latitude', 'longitude'])
+    metadata.add_column('latitude', 'nesreca', sdtype='latitude')
+    metadata.add_column('longitude', 'nesreca', sdtype='longitude')
+    metadata.add_column_relationship('gps', ['latitude', 'longitude'], 'nesreca')
 
     # Run
     table_metadata = metadata.get_table_metadata('nesreca')
diff --git a/tests/integration/metadata/test_visualization.py b/tests/integration/metadata/test_visualization.py
index 2d801ea5d..23a7aee17 100644
--- a/tests/integration/metadata/test_visualization.py
+++ b/tests/integration/metadata/test_visualization.py
@@ -26,9 +26,9 @@ def test_visualize_graph_for_multi_table():
     data2 = pd.DataFrame({'\\|=/bla@#$324%^,"&*()><...': ['a', 'b', 'c']})
     tables = {'1': data1, '2': data2}
     metadata = Metadata.detect_from_dataframes(tables)
-    metadata.update_column('1', '\\|=/bla@#$324%^,"&*()><...', sdtype='id')
-    metadata.update_column('2', '\\|=/bla@#$324%^,"&*()><...', sdtype='id')
-    metadata.set_primary_key('1', '\\|=/bla@#$324%^,"&*()><...')
+    metadata.update_column('\\|=/bla@#$324%^,"&*()><...', '1', sdtype='id')
+    metadata.update_column('\\|=/bla@#$324%^,"&*()><...', '2', sdtype='id')
+    metadata.set_primary_key('\\|=/bla@#$324%^,"&*()><...', '1')
     metadata.add_relationship(
         '1', '2', '\\|=/bla@#$324%^,"&*()><...', '\\|=/bla@#$324%^,"&*()><...'
     )
diff --git a/tests/integration/multi_table/test_hma.py b/tests/integration/multi_table/test_hma.py
index e4ee8e083..e7f2cb2c2 100644
--- a/tests/integration/multi_table/test_hma.py
+++ b/tests/integration/multi_table/test_hma.py
@@ -87,8 +87,8 @@ def test_hma_reset_sampling(self):
         faker = Faker()
         data, metadata = download_demo('multi_table', 'got_families')
         metadata.add_column(
-            'characters',
             'ssn',
+            'characters',
             sdtype='ssn',
         )
         data['characters']['ssn'] = [faker.lexify() for _ in range(len(data['characters']))]
@@ -126,7 +126,7 @@ def test_get_info(self):
         today = datetime.datetime.today().strftime('%Y-%m-%d')
         metadata = Metadata()
         metadata.add_table('tab')
-        metadata.add_column('tab', 'col', sdtype='numerical')
+        metadata.add_column('col', 'tab', sdtype='numerical')
         synthesizer = HMASynthesizer(metadata)
 
         # Run
@@ -221,12 +221,12 @@ def get_custom_constraint_data_and_metadata(self):
 
         metadata = Metadata()
         metadata.detect_table_from_dataframe('parent', parent_data)
-        metadata.update_column('parent', 'primary_key', sdtype='id')
+        metadata.update_column('primary_key', 'parent', sdtype='id')
         metadata.detect_table_from_dataframe('child', child_data)
-        metadata.update_column('child', 'user_id', sdtype='id')
-        metadata.update_column('child', 'id', sdtype='id')
-        metadata.set_primary_key('parent', 'primary_key')
-        metadata.set_primary_key('child', 'id')
+        metadata.update_column('user_id', 'child', sdtype='id')
+        metadata.update_column('id', 'child', sdtype='id')
+        metadata.set_primary_key('primary_key', 'parent')
+        metadata.set_primary_key('id', 'child')
         metadata.add_relationship(
             parent_primary_key='primary_key',
             parent_table_name='parent',
@@ -361,10 +361,10 @@ def test_hma_with_inequality_constraint(self):
 
         metadata = Metadata()
         metadata.detect_table_from_dataframe(table_name='parent_table', data=parent_table)
-        metadata.update_column('parent_table', 'id', sdtype='id')
+        metadata.update_column('id', 'parent_table', sdtype='id')
         metadata.detect_table_from_dataframe(table_name='child_table', data=child_table)
-        metadata.update_column('child_table', 'id', sdtype='id')
-        metadata.update_column('child_table', 'parent_id', sdtype='id')
+        metadata.update_column('id', 'child_table', sdtype='id')
+        metadata.update_column('parent_id', 'child_table', sdtype='id')
 
         metadata.set_primary_key(table_name='parent_table', column_name='id')
         metadata.set_primary_key(table_name='child_table', column_name='id')
@@ -452,14 +452,14 @@ def test_hma_primary_key_and_foreign_key_only(self):
         for table_name, table in data.items():
             metadata.detect_table_from_dataframe(table_name, table)
 
-        metadata.update_column('users', 'user_id', sdtype='id')
-        metadata.update_column('sessions', 'session_id', sdtype='id')
-        metadata.update_column('games', 'game_id', sdtype='id')
-        metadata.update_column('games', 'session_id', sdtype='id')
-        metadata.update_column('games', 'user_id', sdtype='id')
-        metadata.set_primary_key('users', 'user_id')
-        metadata.set_primary_key('sessions', 'session_id')
-        metadata.set_primary_key('games', 'game_id')
+        metadata.update_column('user_id', 'users', sdtype='id')
+        metadata.update_column('session_id', 'sessions', sdtype='id')
+        metadata.update_column('game_id', 'games', sdtype='id')
+        metadata.update_column('session_id', 'games', sdtype='id')
+        metadata.update_column('user_id', 'games', sdtype='id')
+        metadata.set_primary_key('user_id', 'users')
+        metadata.set_primary_key('session_id', 'sessions')
+        metadata.set_primary_key('game_id', 'games')
         metadata.add_relationship('users', 'games', 'user_id', 'user_id')
         metadata.add_relationship('sessions', 'games', 'session_id', 'session_id')
 
@@ -1351,25 +1351,25 @@ def test_null_foreign_keys(self):
         metadata = Metadata()
 
         metadata.add_table('parent_table1')
-        metadata.add_column('parent_table1', 'id', sdtype='id')
-        metadata.set_primary_key('parent_table1', 'id')
+        metadata.add_column('id', 'parent_table1', sdtype='id')
+        metadata.set_primary_key('id', 'parent_table1')
 
         metadata.add_table('parent_table2')
-        metadata.add_column('parent_table2', 'id', sdtype='id')
-        metadata.set_primary_key('parent_table2', 'id')
+        metadata.add_column('id', 'parent_table2', sdtype='id')
+        metadata.set_primary_key('id', 'parent_table2')
 
         metadata.add_table('child_table1')
-        metadata.add_column('child_table1', 'id', sdtype='id')
-        metadata.set_primary_key('child_table1', 'id')
-        metadata.add_column('child_table1', 'fk1', sdtype='id')
-        metadata.add_column('child_table1', 'fk2', sdtype='id')
+        metadata.add_column('id', 'child_table1', sdtype='id')
+        metadata.set_primary_key('id', 'child_table1')
+        metadata.add_column('fk1', 'child_table1', sdtype='id')
+        metadata.add_column('fk2', 'child_table1', sdtype='id')
 
         metadata.add_table('child_table2')
-        metadata.add_column('child_table2', 'id', sdtype='id')
-        metadata.set_primary_key('child_table2', 'id')
-        metadata.add_column('child_table2', 'fk1', sdtype='id')
-        metadata.add_column('child_table2', 'fk2', sdtype='id')
-        metadata.add_column('child_table2', 'cat_type', sdtype='categorical')
+        metadata.add_column('id', 'child_table2', sdtype='id')
+        metadata.set_primary_key('id', 'child_table2')
+        metadata.add_column('fk1', 'child_table2', sdtype='id')
+        metadata.add_column('fk2', 'child_table2', sdtype='id')
+        metadata.add_column('cat_type', 'child_table2', sdtype='categorical')
 
         metadata.add_relationship(
             parent_table_name='parent_table1',
@@ -1842,7 +1842,7 @@ def test_fit_and_sample_numerical_col_names():
         }
     ]
     metadata = Metadata.load_from_dict(metadata_dict)
-    metadata.set_primary_key('0', '1')
+    metadata.set_primary_key('1', '0')
 
     # Run
     synth = HMASynthesizer(metadata)
@@ -1875,11 +1875,11 @@ def test_detect_from_dataframe_numerical_col():
     metadata = Metadata()
     metadata.detect_table_from_dataframe('parent_data', parent_data)
     metadata.detect_table_from_dataframe('child_data', child_data)
-    metadata.update_column('parent_data', '1', sdtype='id')
-    metadata.update_column('child_data', '3', sdtype='id')
-    metadata.update_column('child_data', '4', sdtype='id')
-    metadata.set_primary_key('parent_data', '1')
-    metadata.set_primary_key('child_data', '4')
+    metadata.update_column('1', 'parent_data', sdtype='id')
+    metadata.update_column('3', 'child_data', sdtype='id')
+    metadata.update_column('4', 'child_data', sdtype='id')
+    metadata.set_primary_key('1', 'parent_data')
+    metadata.set_primary_key('4', 'child_data')
     metadata.add_relationship(
         parent_primary_key='1',
         parent_table_name='parent_data',
@@ -1888,11 +1888,11 @@ def test_detect_from_dataframe_numerical_col():
     )
 
     test_metadata = Metadata.detect_from_dataframes(data)
-    test_metadata.update_column('parent_data', '1', sdtype='id')
-    test_metadata.update_column('child_data', '3', sdtype='id')
-    test_metadata.update_column('child_data', '4', sdtype='id')
-    test_metadata.set_primary_key('parent_data', '1')
-    test_metadata.set_primary_key('child_data', '4')
+    test_metadata.update_column('1', 'parent_data', sdtype='id')
+    test_metadata.update_column('3', 'child_data', sdtype='id')
+    test_metadata.update_column('4', 'child_data', sdtype='id')
+    test_metadata.set_primary_key('1', 'parent_data')
+    test_metadata.set_primary_key('4', 'child_data')
     test_metadata.add_relationship(
         parent_primary_key='1',
         parent_table_name='parent_data',
@@ -2005,13 +2005,13 @@ def test_hma_synthesizer_with_fixed_combinations():
     # Creating metadata for the dataset
     metadata = Metadata.detect_from_dataframes(data)
 
-    metadata.update_column('users', 'user_id', sdtype='id')
-    metadata.update_column('records', 'record_id', sdtype='id')
-    metadata.update_column('records', 'user_id', sdtype='id')
-    metadata.update_column('records', 'location_id', sdtype='id')
-    metadata.update_column('locations', 'location_id', sdtype='id')
-    metadata.set_primary_key('users', 'user_id')
-    metadata.set_primary_key('locations', 'location_id')
+    metadata.update_column('user_id', 'users', sdtype='id')
+    metadata.update_column('record_id', 'records', sdtype='id')
+    metadata.update_column('user_id', 'records', sdtype='id')
+    metadata.update_column('location_id', 'records', sdtype='id')
+    metadata.update_column('location_id', 'locations', sdtype='id')
+    metadata.set_primary_key('user_id', 'users')
+    metadata.set_primary_key('location_id', 'locations')
     metadata.add_relationship('users', 'records', 'user_id', 'user_id')
     metadata.add_relationship('locations', 'records', 'location_id', 'location_id')
 
@@ -2053,8 +2053,8 @@ def test_fit_int_primary_key_regex_includes_zero(regex):
         'child_data': child_data,
     }
     metadata = Metadata.detect_from_dataframes(data)
-    metadata.update_column('parent_data', 'parent_id', sdtype='id', regex_format=regex)
-    metadata.set_primary_key('parent_data', 'parent_id')
+    metadata.update_column('parent_id', 'parent_data', sdtype='id', regex_format=regex)
+    metadata.set_primary_key('parent_id', 'parent_data')
 
     # Run and Assert
     instance = HMASynthesizer(metadata)
diff --git a/tests/integration/sequential/test_par.py b/tests/integration/sequential/test_par.py
index 6ae0af54e..620a95cf2 100644
--- a/tests/integration/sequential/test_par.py
+++ b/tests/integration/sequential/test_par.py
@@ -22,9 +22,11 @@ def _get_par_data_and_metadata():
         'context': ['a', 'a', 'b', 'b'],
     })
     metadata = Metadata.detect_from_dataframes({'table': data})
-    metadata.update_column('table', 'entity', sdtype='id')
-    metadata.set_sequence_key('table', 'entity')
-    metadata.set_sequence_index('table', 'date')
+    metadata.update_column('entity', 'table', sdtype='id')
+    metadata.set_sequence_key('entity', 'table')
+
+    metadata.set_sequence_index('date', 'table')
+
     return data, metadata
 
 
@@ -34,9 +36,11 @@ def test_par():
     data = load_demo()
     data['date'] = pd.to_datetime(data['date'])
     metadata = Metadata.detect_from_dataframes({'table': data})
-    metadata.update_column('table', 'store_id', sdtype='id')
-    metadata.set_sequence_key('table', 'store_id')
-    metadata.set_sequence_index('table', 'date')
+    metadata.update_column('store_id', 'table', sdtype='id')
+    metadata.set_sequence_key('store_id', 'table')
+
+    metadata.set_sequence_index('date', 'table')
+
     model = PARSynthesizer(
         metadata=metadata,
         context_columns=['region'],
@@ -67,9 +71,10 @@ def test_column_after_date_simple():
         'col2': ['hello', 'world'],
     })
     metadata = Metadata.detect_from_dataframes({'table': data})
-    metadata.update_column('table', 'col', sdtype='id')
-    metadata.set_sequence_key('table', 'col')
-    metadata.set_sequence_index('table', 'date')
+    metadata.update_column('col', 'table', sdtype='id')
+    metadata.set_sequence_key('col', 'table')
+
+    metadata.set_sequence_index('date', 'table')
 
     # Run
     model = PARSynthesizer(metadata=metadata, epochs=1)
@@ -347,8 +352,10 @@ def test_par_unique_sequence_index_with_enforce_min_max():
     )
     metadata = Metadata.detect_from_dataframes({'table': test_df})
     metadata.update_column(table_name='table', column_name='s_key', sdtype='id')
-    metadata.set_sequence_key('table', 's_key')
-    metadata.set_sequence_index('table', 'visits')
+    metadata.set_sequence_key('s_key', 'table')
+
+    metadata.set_sequence_index('visits', 'table')
+
     synthesizer = PARSynthesizer(
         metadata, enforce_min_max_values=True, enforce_rounding=False, epochs=100, verbose=True
     )
@@ -441,7 +448,7 @@ def test_par_categorical_column_represented_by_floats():
     # Setup
     data, metadata = download_demo('sequential', 'nasdaq100_2019')
     data['category'] = [100.0 if i % 2 == 0 else 50.0 for i in data.index]
-    metadata.add_column('nasdaq100_2019', 'category', sdtype='categorical')
+    metadata.add_column('category', 'nasdaq100_2019', sdtype='categorical')
 
     # Run
     synth = PARSynthesizer(metadata)
diff --git a/tests/integration/single_table/test_base.py b/tests/integration/single_table/test_base.py
index 7ab9bb27c..88265ec1f 100644
--- a/tests/integration/single_table/test_base.py
+++ b/tests/integration/single_table/test_base.py
@@ -93,9 +93,9 @@ def test_sample_from_conditions_with_batch_size():
 
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'column1', sdtype='numerical')
-    metadata.add_column('table', 'column2', sdtype='numerical')
-    metadata.add_column('table', 'column3', sdtype='numerical')
+    metadata.add_column('column1', 'table', sdtype='numerical')
+    metadata.add_column('column2', 'table', sdtype='numerical')
+    metadata.add_column('column3', 'table', sdtype='numerical')
 
     model = GaussianCopulaSynthesizer(metadata)
     model.fit(data)
@@ -120,9 +120,9 @@ def test_sample_from_conditions_negative_float():
 
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'column1', sdtype='numerical')
-    metadata.add_column('table', 'column2', sdtype='numerical')
-    metadata.add_column('table', 'column3', sdtype='numerical')
+    metadata.add_column('column1', 'table', sdtype='numerical')
+    metadata.add_column('column2', 'table', sdtype='numerical')
+    metadata.add_column('column3', 'table', sdtype='numerical')
 
     model = GaussianCopulaSynthesizer(metadata)
     model.fit(data)
@@ -203,7 +203,7 @@ def test_sample_keys_are_scrambled():
     """Test that the keys are scrambled in the sampled data."""
     # Setup
     data, metadata = download_demo(modality='single_table', dataset_name='fake_hotel_guests')
-    metadata.update_column('fake_hotel_guests', 'guest_email', sdtype='id', regex_format='[A-Z]{3}')
+    metadata.update_column('guest_email', 'fake_hotel_guests', sdtype='id', regex_format='[A-Z]{3}')
     synthesizer = GaussianCopulaSynthesizer(metadata)
     synthesizer.fit(data)
 
@@ -234,9 +234,9 @@ def test_multiple_fits():
     })
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'city', sdtype='categorical')
-    metadata.add_column('table', 'state', sdtype='categorical')
-    metadata.add_column('table', 'measurement', sdtype='numerical')
+    metadata.add_column('city', 'table', sdtype='categorical')
+    metadata.add_column('state', 'table', sdtype='categorical')
+    metadata.add_column('measurement', 'table', sdtype='numerical')
     constraint = {
         'constraint_class': 'FixedCombinations',
         'constraint_parameters': {'column_names': ['city', 'state']},
@@ -338,7 +338,7 @@ def test_transformers_correctly_auto_assigned():
     metadata.update_column(
         table_name='table', column_name='primary_key', sdtype='id', regex_format='user-[0-9]{3}'
     )
-    metadata.set_primary_key('table', 'primary_key')
+    metadata.set_primary_key('primary_key', 'table')
     metadata.update_column(table_name='table', column_name='pii_col', sdtype='address', pii=True)
     synthesizer = GaussianCopulaSynthesizer(
         metadata, enforce_min_max_values=False, enforce_rounding=False
@@ -428,7 +428,7 @@ def test_auto_assign_transformers_and_update_with_pii():
     # Run
     metadata.update_column(table_name='table', column_name='id', sdtype='first_name')
     metadata.update_column(table_name='table', column_name='name', sdtype='name')
-    metadata.set_primary_key('table', 'id')
+    metadata.set_primary_key('id', 'table')
     synthesizer = GaussianCopulaSynthesizer(metadata)
     synthesizer.auto_assign_transformers(data)
 
@@ -457,8 +457,8 @@ def test_refitting_a_model():
 
     metadata = Metadata.detect_from_dataframes({'table': data})
     metadata.update_column(table_name='table', column_name='name', sdtype='name')
-    metadata.update_column('table', 'id', sdtype='id')
-    metadata.set_primary_key('table', 'id')
+    metadata.update_column('id', 'table', sdtype='id')
+    metadata.set_primary_key('id', 'table')
 
     synthesizer = GaussianCopulaSynthesizer(metadata)
     synthesizer.fit(data)
@@ -483,7 +483,7 @@ def test_get_info():
     today = datetime.datetime.today().strftime('%Y-%m-%d')
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'col', sdtype='numerical')
+    metadata.add_column('col', 'table', sdtype='numerical')
     synthesizer = GaussianCopulaSynthesizer(metadata)
 
     # Run
@@ -628,7 +628,7 @@ def test_metadata_updated_no_warning(mock__fit, tmp_path):
 
     # Run 3
     instance = BaseSingleTableSynthesizer(metadata_detect)
-    metadata_detect.update_column('mock_table', 'col 1', sdtype='categorical')
+    metadata_detect.update_column('col 1', 'mock_table', sdtype='categorical')
     file_name = tmp_path / 'singletable_2.json'
     metadata_detect.save_to_json(file_name)
     with warnings.catch_warnings(record=True) as captured_warnings:
diff --git a/tests/integration/single_table/test_constraints.py b/tests/integration/single_table/test_constraints.py
index 3477d4557..6e7a8c9e0 100644
--- a/tests/integration/single_table/test_constraints.py
+++ b/tests/integration/single_table/test_constraints.py
@@ -74,9 +74,9 @@ def test_fit_with_unique_constraint_on_data_with_only_index_column():
 
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'key', sdtype='id')
-    metadata.add_column('table', 'index', sdtype='categorical')
-    metadata.set_primary_key('table', 'key')
+    metadata.add_column('key', 'table', sdtype='id')
+    metadata.add_column('index', 'table', sdtype='categorical')
+    metadata.set_primary_key('key', 'table')
 
     model = GaussianCopulaSynthesizer(metadata)
     constraint = {
@@ -139,10 +139,10 @@ def test_fit_with_unique_constraint_on_data_which_has_index_column():
 
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'key', sdtype='id')
-    metadata.add_column('table', 'index', sdtype='categorical')
-    metadata.add_column('table', 'test_column', sdtype='categorical')
-    metadata.set_primary_key('table', 'key')
+    metadata.add_column('key', 'table', sdtype='id')
+    metadata.add_column('index', 'table', sdtype='categorical')
+    metadata.add_column('test_column', 'table', sdtype='categorical')
+    metadata.set_primary_key('key', 'table')
 
     model = GaussianCopulaSynthesizer(metadata)
     constraint = {
@@ -198,9 +198,9 @@ def test_fit_with_unique_constraint_on_data_subset():
 
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'key', sdtype='id')
-    metadata.add_column('table', 'test_column', sdtype='categorical')
-    metadata.set_primary_key('table', 'key')
+    metadata.add_column('key', 'table', sdtype='id')
+    metadata.add_column('test_column', 'table', sdtype='categorical')
+    metadata.set_primary_key('key', 'table')
 
     test_df = test_df.iloc[[1, 3, 4]]
     constraint = {
@@ -295,9 +295,9 @@ def test_conditional_sampling_constraint_uses_reject_sampling(gm_mock, isinstanc
 
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'city', sdtype='categorical')
-    metadata.add_column('table', 'state', sdtype='categorical')
-    metadata.add_column('table', 'age', sdtype='numerical')
+    metadata.add_column('city', 'table', sdtype='categorical')
+    metadata.add_column('state', 'table', sdtype='categorical')
+    metadata.add_column('age', 'table', sdtype='numerical')
 
     model = GaussianCopulaSynthesizer(metadata)
 
@@ -815,8 +815,8 @@ def reverse_transform(column_names, data):
         'other': [7, 8, 9],
     })
     metadata = Metadata.detect_from_dataframes({'table': data})
-    metadata.update_column('table', 'key', sdtype='id', regex_format=r'\w_\d')
-    metadata.set_primary_key('table', 'key')
+    metadata.update_column('key', 'table', sdtype='id', regex_format=r'\w_\d')
+    metadata.set_primary_key('key', 'table')
     synth = GaussianCopulaSynthesizer(metadata)
     synth.add_custom_constraint_class(custom_constraint, 'custom')
 
@@ -845,8 +845,8 @@ def test_timezone_aware_constraints():
 
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'col1', sdtype='datetime')
-    metadata.add_column('table', 'col2', sdtype='datetime')
+    metadata.add_column('col1', 'table', sdtype='datetime')
+    metadata.add_column('col2', 'table', sdtype='datetime')
 
     my_constraint = {
         'constraint_class': 'Inequality',
diff --git a/tests/integration/single_table/test_ctgan.py b/tests/integration/single_table/test_ctgan.py
index 9f892f878..0f87c5fe7 100644
--- a/tests/integration/single_table/test_ctgan.py
+++ b/tests/integration/single_table/test_ctgan.py
@@ -17,12 +17,12 @@ def test__estimate_num_columns():
     # Setup
     metadata = Metadata()
     metadata.add_table('table')
-    metadata.add_column('table', 'numerical', sdtype='numerical')
-    metadata.add_column('table', 'categorical', sdtype='categorical')
-    metadata.add_column('table', 'categorical2', sdtype='categorical')
-    metadata.add_column('table', 'categorical3', sdtype='categorical')
-    metadata.add_column('table', 'datetime', sdtype='datetime')
-    metadata.add_column('table', 'boolean', sdtype='boolean')
+    metadata.add_column('numerical', 'table', sdtype='numerical')
+    metadata.add_column('categorical', 'table', sdtype='categorical')
+    metadata.add_column('categorical2', 'table', sdtype='categorical')
+    metadata.add_column('categorical3', 'table', sdtype='categorical')
+    metadata.add_column('datetime', 'table', sdtype='datetime')
+    metadata.add_column('boolean', 'table', sdtype='boolean')
     data = pd.DataFrame({
         'numerical': [0.1, 0.2, 0.3],
         'datetime': ['2020-01-01', '2020-01-02', '2020-01-03'],