diff --git a/applications/qmc/sse4/model.h b/applications/qmc/sse4/model.h
index 3146c0adb..17f8aecc8 100644
--- a/applications/qmc/sse4/model.h
+++ b/applications/qmc/sse4/model.h
@@ -90,19 +90,6 @@ class Model {
     _lowering_matrix_elements.resize(lattice.max_site_type() + 1);
 
     construct_vertices();
-
-    if (epsilon <= 0.0 && model.is_signed()) {
-        epsilon = *std::max_element(
-            _max_diag_me.begin(),
-            _max_diag_me.end()
-        );
-
-        std::cout
-            << "Warning: Hamiltonian has a sign problem and EPSILON<=0.\n"
-            << "Automatically setting EPSILON = "
-            << epsilon
-            << " (largest diagonal matrix element).\n";
-    }
 	}
     
     std::vector<unsigned> const& nbstates() const
@@ -289,8 +276,7 @@ class Model {
             unsigned nneighbors0 = lattice.nneighbors(sites[0]);
             unsigned nneighbors1 = lattice.nneighbors(sites[1]);
             
-            // _max_diag_me[i] = std::numeric_limits<double>::min();
-	    _max_diag_me[i] = std::numeric_limits<double>::lowest();
+            _max_diag_me[i] = std::numeric_limits<double>::lowest();
             
             for (unsigned l = 0; l < nstates[i]; ++l) {
                 vertex_type vertex;
@@ -339,9 +325,26 @@ class Model {
         if (epsilon == 0.0 && !have_diagonal)
             throw std::runtime_error("Hamiltonian looks purely off-diagonal. "
                 "Parameter EPSILON has to be non zero for SSE to work.");
-                
-        if (epsilon <= 0.0)
-            epsilon = 1e-6;
+        if (epsilon <= 0.0) {
+            if (model.is_signed()) {
+                // A tiny EPSILON can make the diagonal update effectively
+                // non-ergodic for signed models. Use the largest positive
+                // diagonal matrix element once those elements are known.
+                epsilon = 1e-6;
+                for (std::vector<double>::const_iterator it = _max_diag_me.begin();
+                        it != _max_diag_me.end(); ++it)
+                    if (*it > epsilon)
+                        epsilon = *it;
+
+                std::cout
+                    << "Warning: Hamiltonian has a sign problem and EPSILON<=0.\n"
+                    << "Automatically setting EPSILON = " << epsilon
+                    << " (largest positive diagonal matrix element, with a "
+                       "1e-6 minimum).\n";
+            } else {
+                epsilon = 1e-6;
+            }
+        }
         
         std::set<unsigned>::const_iterator sti = site_types.begin();
         for (; sti != site_types.end(); ++sti)