diff --git a/Util/exact_riemann/README.md b/Util/exact_riemann/README.md
index ada8e281ec..013a81693a 100644
--- a/Util/exact_riemann/README.md
+++ b/Util/exact_riemann/README.md
@@ -12,3 +12,14 @@ https://ui.adsabs.harvard.edu/abs/2015ApJS..216...31Z/abstract
 and more details are given there.
 
 To build the solver, simply type 'make' in this directory.
+
+
+Notes:
+
+* ``test2`` is a vacuum
+
+  The velocity in the star region should be 0, but it seems that
+  slight differences in the rarefaction integration from the left and
+  from the right give different roundoff, resulting in a small, finite
+  velocity.  This can be controlled a bit by tightening the tolerance
+  in the rarefaction integration.
diff --git a/Util/exact_riemann/riemann_star_state.H b/Util/exact_riemann/riemann_star_state.H
index 2448247129..31e1952722 100644
--- a/Util/exact_riemann/riemann_star_state.H
+++ b/Util/exact_riemann/riemann_star_state.H
@@ -142,12 +142,11 @@ riemann_star_state(const amrex::Real rho_l, const amrex::Real u_l, const amrex::
 
         amrex::Real pstar_new = pstar - Z_l * Z_r * (ustar_r - ustar_l) / (Z_l + Z_r);
 
-        // estimate the error in the current star solution
-        amrex::Real err1 = std::abs(ustar_r - ustar_l);
-        amrex::Real err2 = pstar_new - pstar;
+        // estimate the error in the current pstar solution
 
-        if (err1 < tol * amrex::max(std::abs(ustar_l), std::abs(ustar_r)) &&
-            err2 < tol * pstar) {
+        amrex::Real error = std::abs(pstar_new - pstar);
+
+        if (error < tol * pstar) {
             converged = true;
         }