diff --git a/lslopt/lslfoldconst.py b/lslopt/lslfoldconst.py
index a22e3a5..92a99b2 100644
--- a/lslopt/lslfoldconst.py
+++ b/lslopt/lslfoldconst.py
@@ -300,14 +300,12 @@ class foldconst(object):
                 parent[index] = child[0]['ch'][0]
                 return
 
-        if nt == 'NEG':
-            # bool(-a) equals bool(a)
-            parent[index] = child[0]
-            self.FoldCond(parent, index, ParentIsNegation)
-            return
-
-        if nt in self.binary_ops and child[0]['t'] == child[1]['t'] == 'integer':
-            if nt == '!=':
+            if (child[0]['nt'] == '==' and child[0]['ch'][0]['t'] == 'integer'
+                and child[0]['ch'][1]['t'] == 'integer'
+               ):
+                # We have !(int == int). Replace with int ^ int or with int - 1
+                node = parent[index] = child[0]  # remove the negation
+                child = child[0]['ch']
                 if child[0]['nt'] == 'CONST' and child[0]['value'] == 1 \
                    or child[1]['nt'] == 'CONST' and child[1]['value'] == 1:
                     # a != 1  ->  a - 1  (which FoldTree will transform to ~-a)
@@ -319,6 +317,14 @@ class foldconst(object):
                 self.FoldTree(parent, index)
                 return
 
+
+        if nt == 'NEG':
+            # bool(-a) equals bool(a)
+            parent[index] = child[0]
+            self.FoldCond(parent, index, ParentIsNegation)
+            return
+
+        if nt in self.binary_ops and child[0]['t'] == child[1]['t'] == 'integer':
             if nt == '==':
                 if child[0]['nt'] == 'CONST' and -1 <= child[0]['value'] <= 1 \
                    or child[1]['nt'] == 'CONST' and -1 <= child[1]['value'] <= 1:
@@ -702,7 +708,7 @@ class foldconst(object):
                     subexpr['ch'] = [subexpr['ch'][b], subexpr['ch'][a]]
                     parent[index] = subexpr
                     return
-            if snt == '!=':
+            if snt == '!=' or snt == '^':
                 subexpr['nt'] = '=='
                 parent[index] = subexpr
                 self.FoldTree(parent, index)