diff --git a/burnman/tools/polytope.py b/burnman/tools/polytope.py
index b4b833e8..c8471679 100644
--- a/burnman/tools/polytope.py
+++ b/burnman/tools/polytope.py
@@ -179,6 +179,10 @@ def simplify_composite_with_composition(composite, composition):
     solutions, this function will return a composite that only contains
     the Mg-bearing endmembers.
 
+    If the solutions have endmember proportions that are consistent with the
+    bulk composition, the site occupancies of the new solution models are set to
+    the values in the original models.
+
     :param composite: The initial Composite object.
     :type composite: :class:`burnman.Composite` object
 
@@ -239,7 +243,24 @@ def simplify_composite_with_composition(composite, composition):
                     )
 
                     composite_changed = True
-                    soln = transform_solution_to_new_basis(ph, new_basis)
+
+                    # If the composition is set and
+                    # consistent with the new basis,
+                    # make a new solution with the composition
+                    # already set.
+                    try:
+                        sol = np.linalg.lstsq(
+                            new_basis.T, ph.molar_fractions, rcond=None
+                        )
+                        if sol[1][0] > 1.0e-10:
+                            f = None
+                        else:
+                            f = sol[0]
+                    except AttributeError:
+                        f = None
+                    soln = transform_solution_to_new_basis(
+                        ph, new_basis, molar_fractions=f
+                    )
                     new_phases.append(soln)
                 else:
                     logging.info(
diff --git a/tests/test_polytope.py b/tests/test_polytope.py
index ec52fbfe..d6b89d50 100644
--- a/tests/test_polytope.py
+++ b/tests/test_polytope.py
@@ -47,6 +47,21 @@ def test_simplify_composite(self):
         self.assertEqual(strings[0], "[Fe]3[Mg][Si]")
         self.assertEqual(strings[1], "[Mg]3[Mg][Si]")
 
+    def test_simplify_composite_and_composition(self):
+        gt = SLB_2011.garnet()
+        gt.set_composition([-0.1, 0.1, 0.0, 1.0, 0.0])
+        ol = SLB_2011.mg_fe_olivine()
+        assemblage = Composite([ol, gt], [0.7, 0.3])
+        composition = {"Fe": 3.0, "Mg": 1.0, "Si": 3.9, "O": 11.8}
+
+        new_assemblage = simplify_composite_with_composition(assemblage, composition)
+        new_gt = new_assemblage.phases[1]
+        self.assertTrue(new_gt.n_endmembers == 2)
+        strings = list(sorted([e[1] for e in new_gt.endmembers]))
+        self.assertEqual(strings[0], "[Fe]3[Mg][Si]")
+        self.assertEqual(strings[1], "[Mg]3[Mg][Si]")
+        self.assertArraysAlmostEqual([0.1, 0.9], new_gt.molar_fractions)
+
 
 if __name__ == "__main__":
     unittest.main()