diff --git a/.github/workflows/bump-version.yml b/.github/workflows/bump-version.yml
index 71a14ea3e7..e574a2ab34 100644
--- a/.github/workflows/bump-version.yml
+++ b/.github/workflows/bump-version.yml
@@ -204,7 +204,6 @@ jobs:
     - name: Install Python dependencies
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip install --system tbump
         python -m pip list
 
diff --git a/.github/workflows/ci-windows.yml b/.github/workflows/ci-windows.yml
index 3a75d9e3ab..b625754baf 100644
--- a/.github/workflows/ci-windows.yml
+++ b/.github/workflows/ci-windows.yml
@@ -33,7 +33,6 @@ jobs:
     - name: Install dependencies
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip install --system --upgrade '.[all,test]'
 
     - name: List installed Python packages
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 5482e8a9d0..28a449ab63 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -50,14 +50,13 @@ jobs:
       if: matrix.python-version != '3.8'
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip install --system --upgrade ".[all,test]"
 
       # c.f. https://github.com/astral-sh/uv/issues/2062
     - name: Install dependencies (Python 3.8)
       if: matrix.python-version == '3.8'
       run: |
-        python -m pip install --upgrade pip wheel
+        python -m pip install --upgrade pip
         python -m pip install --upgrade ".[all,test]"
 
     - name: List installed Python packages
diff --git a/.github/workflows/dependencies-head.yml b/.github/workflows/dependencies-head.yml
index 403695b65e..c714392d81 100644
--- a/.github/workflows/dependencies-head.yml
+++ b/.github/workflows/dependencies-head.yml
@@ -33,7 +33,6 @@ jobs:
     - name: Install dependencies
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip --no-cache --quiet install --system --upgrade --pre ".[all,test]"
         python -m pip list
 
@@ -64,7 +63,6 @@ jobs:
     - name: Install dependencies
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip --no-cache --quiet install --system --upgrade ".[all,test]"
         uv pip uninstall --system scipy
         # uv wants to upgrade dependencies (numpy) to a dev release too, so don't --upgrade
@@ -92,7 +90,6 @@ jobs:
     - name: Install dependencies
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip --no-cache --quiet install --system --upgrade ".[all,test]"
         uv pip uninstall --system iminuit
         uv pip install --system --upgrade cython
@@ -119,7 +116,6 @@ jobs:
     - name: Install dependencies
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip --no-cache --quiet install --system --upgrade ".[all,test]"
         uv pip uninstall --system uproot
         uv pip install --system --upgrade git+https://github.com/scikit-hep/uproot5.git
@@ -147,7 +143,6 @@ jobs:
     - name: Install dependencies
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip --no-cache --quiet install --system --upgrade ".[all,test]"
         uv pip uninstall --system matplotlib
         # Need to use --extra-index-url as all dependencies aren't on scientific-python-nightly-wheels package index.
@@ -184,7 +179,6 @@ jobs:
     - name: Install dependencies
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip --no-cache --quiet install --system --upgrade ".[all,test]"
         uv pip uninstall --system pytest
         uv pip install --system --upgrade git+https://github.com/pytest-dev/pytest.git
diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml
index 11251ae136..c7a99fda4d 100644
--- a/.github/workflows/docs.yml
+++ b/.github/workflows/docs.yml
@@ -32,7 +32,6 @@ jobs:
     - name: Install Python dependencies
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip --quiet install --system --upgrade ".[docs,test]"
         uv pip install --system yq
         python -m pip list
diff --git a/.github/workflows/lower-bound-requirements.yml b/.github/workflows/lower-bound-requirements.yml
index 87305d10a8..5bdd837c68 100644
--- a/.github/workflows/lower-bound-requirements.yml
+++ b/.github/workflows/lower-bound-requirements.yml
@@ -30,7 +30,7 @@ jobs:
     - name: Install dependencies and force lowest bound
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip 'setuptools<70.0.0' wheel
+        uv pip install --system --upgrade 'setuptools<70.0.0'
         uv pip --no-cache install --system --constraint tests/constraints.txt ".[all,test]"
 
     - name: List installed Python packages
diff --git a/.github/workflows/notebooks.yml b/.github/workflows/notebooks.yml
index 91439d0f8f..52b6fb1af4 100644
--- a/.github/workflows/notebooks.yml
+++ b/.github/workflows/notebooks.yml
@@ -32,7 +32,6 @@ jobs:
     - name: Install dependencies
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         # FIXME: c.f. https://github.com/scikit-hep/pyhf/issues/2104
         uv pip install --system --upgrade ".[all,test]" 'jupyter-client<8.0.0'
 
diff --git a/.github/workflows/release_tests.yml b/.github/workflows/release_tests.yml
index f3312c8c9e..0569562704 100644
--- a/.github/workflows/release_tests.yml
+++ b/.github/workflows/release_tests.yml
@@ -41,7 +41,6 @@ jobs:
     - name: Install from PyPI
       run: |
         python -m pip install uv
-        uv pip install --system --upgrade pip wheel
         uv pip install --system --pre 'pyhf[backends,xmlio]'
         uv pip install --system pytest
         python -m pip list
diff --git a/docker/Dockerfile b/docker/Dockerfile
index ba7c8f5ab5..1e81d375c4 100644
--- a/docker/Dockerfile
+++ b/docker/Dockerfile
@@ -17,7 +17,6 @@ RUN apt-get -qq -y update && \
     . /usr/local/venv/bin/activate && \
     cd /code && \
     python -m pip --no-cache-dir install --upgrade uv && \
-    uv pip install --no-cache --upgrade pip wheel && \
     uv pip install --no-cache '.[xmlio,contrib]' && \
     uv pip list