diff --git a/src/elexsolver/TransitionSolver.py b/src/elexsolver/TransitionSolver.py
index 945da4ea..dd3facab 100644
--- a/src/elexsolver/TransitionSolver.py
+++ b/src/elexsolver/TransitionSolver.py
@@ -45,10 +45,14 @@ def _check_percentages(self, A: np.ndarray):
 
     def _check_and_rescale(self, A: np.ndarray):
         """
-        Rescale columns (units) so that they sum to 1 (100%).
+        After ensuring that A is (things x units), make sure we have enough units.
+        If that's the case, rescale columns (units) so that they sum to 1 (100%).
         """
+        if A.shape[1] <= A.shape[0] or (A.shape[1] // 2) <= A.shape[0]:
+            raise ValueError(f"Not enough units ({A.shape[1]}) relative to the number of things ({A.shape[0]}).")
+
         if not np.all(A.sum(axis=0) == 1):
-            LOG.warn("Each column (unit) needs to sum to 1.  Rescaling...")
+            LOG.warn("Each unit needs to sum to 1.  Rescaling...")
             if isinstance(A, np.ndarray):
                 for j in range(0, A.shape[1]):
                     A[:, j] /= A[:, j].sum()