diff --git a/src/sat/sat_bdd.cpp b/src/sat/sat_bdd.cpp
index 4835b8580..36900760e 100644
--- a/src/sat/sat_bdd.cpp
+++ b/src/sat/sat_bdd.cpp
@@ -94,8 +94,8 @@ namespace sat {
 
     bool bdd_manager::check_result(op_entry*& e1, op_entry const* e2, BDD a, BDD b, BDD c) {
         if (e1 != e2) {
+            push_entry(e1);
             if (e2->m_bdd1 == a && e2->m_bdd2 == b && e2->m_op == c) {
-                push_entry(e1);
                 return true;
             }
             e1 = const_cast<op_entry*>(e2);
@@ -343,12 +343,15 @@ namespace sat {
 
     bdd_manager::BDD bdd_manager::mk_quant_rec(unsigned l, BDD b, bdd_op op) {
         unsigned lvl = level(b);
-        
-        if (lvl == l) {
-            return apply(lo(b), hi(b), op);
+        BDD r;
+        if (is_const(b)) {
+            r = b;
+        }
+        else if (lvl == l) {
+            r = apply(lo(b), hi(b), op);
         }
         else if (lvl < l) {
-            return b;
+            r = b;
         }
         else {
             BDD a = level2bdd(l);
@@ -356,14 +359,16 @@ namespace sat {
             op_entry * e1 = pop_entry(a, b, q_op);
             op_entry const* e2 = m_op_cache.insert_if_not_there(e1);
             if (check_result(e1, e2, a, b, q_op)) 
-                return e2->m_result;
-            push(mk_quant_rec(l, lo(b), op));
-            push(mk_quant_rec(l, hi(b), op));
-            BDD r = make_node(lvl, read(2), read(1));
-            pop(2);
-            e1->m_result = r;
-            return r;
+                r = e2->m_result;
+            else {
+                push(mk_quant_rec(l, lo(b), op));
+                push(mk_quant_rec(l, hi(b), op));
+                r = make_node(lvl, read(2), read(1));
+                pop(2);
+                e1->m_result = r;
+            }
         }
+        return r;
     }
 
     double bdd_manager::count(bdd const& b, unsigned z) {
@@ -495,7 +500,7 @@ namespace sat {
         return out;
     }
 
-    bdd::bdd(int root, bdd_manager* m): root(root), m(m) { m->inc_ref(root); }
+    bdd::bdd(unsigned root, bdd_manager* m): root(root), m(m) { m->inc_ref(root); }
     bdd::bdd(bdd & other): root(other.root), m(other.m) { m->inc_ref(root); }
     bdd::~bdd() { m->dec_ref(root); }
     bdd bdd::lo() const { return bdd(m->lo(root), m); }
@@ -506,7 +511,7 @@ namespace sat {
     bdd bdd::operator!() { return m->mk_not(*this); }
     bdd bdd::operator&&(bdd const& other) { return m->mk_and(*this, other); }
     bdd bdd::operator||(bdd const& other) { return m->mk_or(*this, other); }
-    bdd& bdd::operator=(bdd const& other) { int r1 = root; root = other.root; m->inc_ref(root); m->dec_ref(r1); return *this; }
+    bdd& bdd::operator=(bdd const& other) { unsigned r1 = root; root = other.root; m->inc_ref(root); m->dec_ref(r1); return *this; }
     std::ostream& bdd::display(std::ostream& out) const { return m->display(out, *this); }
     std::ostream& operator<<(std::ostream& out, bdd const& b) { return b.display(out); }
 
diff --git a/src/sat/sat_bdd.h b/src/sat/sat_bdd.h
index da26c0b36..29d91446e 100644
--- a/src/sat/sat_bdd.h
+++ b/src/sat/sat_bdd.h
@@ -29,9 +29,9 @@ namespace sat {
 
     class bdd {
         friend class bdd_manager;
-        int          root;
+        unsigned     root;
         bdd_manager* m;
-        bdd(int root, bdd_manager* m);
+        bdd(unsigned root, bdd_manager* m);
     public:
         bdd(bdd & other);
         bdd& operator=(bdd const& other);
@@ -57,7 +57,7 @@ namespace sat {
     class bdd_manager {
         friend bdd;
 
-        typedef int BDD;
+        typedef unsigned BDD;
 
         enum bdd_op {
             bdd_and_op = 2,
@@ -70,7 +70,7 @@ namespace sat {
         };
 
         struct bdd_node {
-            bdd_node(unsigned level, int lo, int hi):
+            bdd_node(unsigned level, BDD lo, BDD hi):
                 m_refcount(0),
                 m_level(level),
                 m_lo(lo),
@@ -80,8 +80,8 @@ namespace sat {
             bdd_node(): m_level(0), m_lo(0), m_hi(0), m_index(0) {}
             unsigned m_refcount : 10;
             unsigned m_level : 22;
-            int      m_lo;
-            int      m_hi;
+            BDD      m_lo;
+            BDD      m_hi;
             unsigned m_index;
             unsigned hash() const { return mk_mix(m_level, m_lo, m_hi); }
         };
@@ -176,7 +176,7 @@ namespace sat {
 
         inline bool is_true(BDD b) const { return b == true_bdd; }
         inline bool is_false(BDD b) const { return b == false_bdd; }
-        inline bool is_const(BDD b) const { return 0 <= b && b <= 1; }
+        inline bool is_const(BDD b) const { return b <= 1; }
         inline unsigned level(BDD b) const { return m_nodes[b].m_level; }
         inline unsigned var(BDD b) const { return m_level2var[level(b)]; }
         inline BDD lo(BDD b) const { return m_nodes[b].m_lo; }
diff --git a/src/test/bdd.cpp b/src/test/bdd.cpp
index 319f05bf8..f3f6e6b8d 100644
--- a/src/test/bdd.cpp
+++ b/src/test/bdd.cpp
@@ -33,9 +33,34 @@ namespace sat {
         SASSERT(!(v0 && v1) == (!v0 || !v1));
         SASSERT(!(v0 || v1) == (!v0 && !v1));
     }
+
+    static void test3() {
+        bdd_manager m(20, 1000);
+        bdd v0 = m.mk_var(0);
+        bdd v1 = m.mk_var(1);
+        bdd v2 = m.mk_var(2);
+        bdd c1 = (v0 && v1) || v2;
+        bdd c2 = m.mk_exists(0, c1);
+        std::cout << c1 << "\n";
+        std::cout << c2 << "\n";
+        SASSERT(c2 == (v1 || v2));
+        c2 = m.mk_exists(1, c1);
+        SASSERT(c2 == (v0 || v2));
+        c2 = m.mk_exists(2, c1);
+        SASSERT(c2.is_true());
+        SASSERT(m.mk_exists(3, c1) == c1);
+        c1 = (v0 && v1) || (v1 && v2) || (!v0 && !v2);
+        c2 = m.mk_exists(0, c1);
+        SASSERT(c2 == (v1 || (v1 && v2) || !v2));
+        c2 = m.mk_exists(1, c1);
+        SASSERT(c2 == (v0 || v2 || (!v0 && !v2)));
+        c2 = m.mk_exists(2, c1);
+        SASSERT(c2 == ((v0 && v1) || v1 || !v0));
+    }
 }
 
 void tst_bdd() {
     sat::test1();
     sat::test2();
+    sat::test3();
 }