diff --git a/pyomo/repn/standard_repn.py b/pyomo/repn/standard_repn.py
index d615dd5c82a..b543f264e59 100644
--- a/pyomo/repn/standard_repn.py
+++ b/pyomo/repn/standard_repn.py
@@ -743,12 +743,19 @@ def _collect_pow(exp, multiplier, idMap, compute_values, verbose, quadratic):
                                 or res.constant != 0)
                 if has_constant:
                     ans.constant = multiplier*res.constant*res.constant
-                while len(res.linear) > 0:
-                    key1, coef1 = res.linear.popitem()
+
+                # this is reversed since we want to pop off the end for efficiency
+                # and the quadratic terms have a convention that the indexing tuple
+                # of key1, key2 is such that key1 <= key2
+                keys = sorted(res.linear.keys(), reverse=True)
+                while len(keys) > 0:
+                    key1 = keys.pop()
+                    coef1 = res.linear[key1]
                     if has_constant:
                         ans.linear[key1] = 2*multiplier*coef1*res.constant
                     ans.quadratic[key1,key1] = multiplier*coef1*coef1
-                    for key2, coef2 in res.linear.items():
+                    for key2 in keys:
+                        coef2 = res.linear[key2]
                         ans.quadratic[key1,key2] = 2*multiplier*coef1*coef2
                 return ans