diff --git a/src/ast/rewriter/pb2bv_rewriter.cpp b/src/ast/rewriter/pb2bv_rewriter.cpp
index f546ef70b..d85bdec41 100644
--- a/src/ast/rewriter/pb2bv_rewriter.cpp
+++ b/src/ast/rewriter/pb2bv_rewriter.cpp
@@ -5,7 +5,7 @@ Module Name:
 
     pb2bv_rewriter.cpp
 
-Abstract:
+Abstralct:
 
     Conversion from pseudo-booleans to bit-vectors.
 
@@ -25,6 +25,7 @@ Notes:
 #include"ast_util.h"
 #include"ast_pp.h"
 #include"lbool.h"
+#include"uint_set.h"
 
 const unsigned g_primes[7] = { 2, 3, 5, 7, 11, 13, 17};
 
@@ -111,7 +112,13 @@ struct pb2bv_rewriter::imp {
             if (k.is_neg()) {
                 return expr_ref((is_le == l_false)?m.mk_true():m.mk_false(), m);
             }
-            
+
+            expr_ref result(m);
+            switch (is_le) {
+            case l_true:  if (mk_le_tot(sz, args, k, result)) return result; else break;
+            case l_false: if (mk_ge_tot(sz, args, k, result)) return result; else break;
+            case l_undef: break;
+            }
 #if 0
             expr_ref result(m);
             switch (is_le) {
@@ -172,6 +179,141 @@ struct pb2bv_rewriter::imp {
             }
         }
 
+        /**
+           \brief Totalizer encoding. Based on a version by Miguel.
+         */
+
+        bool mk_le_tot(unsigned sz, expr * const * args, rational const& _k, expr_ref& result) {
+            SASSERT(sz == m_coeffs.size());
+            if (!_k.is_unsigned() || sz == 0) return false;
+            unsigned k = _k.get_unsigned();
+            expr_ref_vector args1(m);
+            rational bound;
+            flip(sz, args, args1, _k, bound);
+            if (bound.get_unsigned() < k) {
+                return mk_ge_tot(sz, args1.c_ptr(), bound, result);
+            }
+            if (k > 20) {
+                return false;
+            }
+            result = m.mk_not(bounded_addition(sz, args, k + 1));
+            TRACE("pb", tout << result << "\n";);
+            return true;
+        }
+
+        bool mk_ge_tot(unsigned sz, expr * const * args, rational const& _k, expr_ref& result) {
+            SASSERT(sz == m_coeffs.size());
+            if (!_k.is_unsigned() || sz == 0) return false;
+            unsigned k = _k.get_unsigned();
+            expr_ref_vector args1(m);
+            rational bound;
+            flip(sz, args, args1, _k, bound);
+            if (bound.get_unsigned() < k) {
+                return mk_le_tot(sz, args1.c_ptr(), bound, result);
+            }
+            if (k > 20) {
+                return false;
+            }
+            result = bounded_addition(sz, args, k);
+            TRACE("pb", tout << result << "\n";);
+            return true;
+        }
+
+        void flip(unsigned sz, expr* const* args, expr_ref_vector& args1, rational const& k, rational& bound) {
+            bound = -k;
+            for (unsigned i = 0; i < sz; ++i) {
+                args1.push_back(mk_not(args[i]));
+                bound += m_coeffs[i];
+            }
+        }
+
+        expr_ref bounded_addition(unsigned sz, expr * const * args, unsigned k) {
+            SASSERT(sz > 0);
+            expr_ref result(m);
+            vector<expr_ref_vector> es;
+            vector<unsigned_vector> coeffs;
+            for (unsigned i = 0; i < m_coeffs.size(); ++i) {
+                unsigned_vector v;
+                expr_ref_vector e(m);
+                unsigned c = m_coeffs[i].get_unsigned();
+                v.push_back(c >= k ? k : c);
+                e.push_back(args[i]);   
+                es.push_back(e);
+                coeffs.push_back(v);
+            }
+            while (es.size() > 1) {
+                for (unsigned i = 0; i + 1 < es.size(); i += 2) {
+                    expr_ref_vector o(m);
+                    unsigned_vector oc;
+                    tot_adder(es[i], coeffs[i], es[i + 1], coeffs[i + 1], k, o, oc);
+                    es[i / 2].set(o);
+                    coeffs[i / 2] = oc;
+                }
+                if ((es.size() % 2) == 1) {
+                    es[es.size() / 2].set(es.back());
+                    coeffs[es.size() / 2] = coeffs.back();
+                }
+                es.shrink((1 + es.size())/2);
+                coeffs.shrink((1 + coeffs.size())/2);
+            }
+            SASSERT(coeffs.size() == 1);
+            SASSERT(coeffs[0].back() <= k);
+            if (coeffs[0].back() == k) {
+                result = es[0].back();
+            }
+            else {
+                result = m.mk_false();
+            }
+            return result;
+        }
+
+        void tot_adder(expr_ref_vector const& l, unsigned_vector const& lc,
+                       expr_ref_vector const& r, unsigned_vector const& rc,
+                       unsigned k,
+                       expr_ref_vector& o, unsigned_vector & oc) {
+            SASSERT(l.size() == lc.size());
+            SASSERT(r.size() == rc.size());
+            uint_set sums;
+            vector<expr_ref_vector> trail;
+            u_map<unsigned> sum2def;
+            for (unsigned i = 0; i <= l.size(); ++i) {
+                for (unsigned j = (i == 0) ? 1 : 0; j <= r.size(); ++j) {
+                    unsigned sum = std::min(k, ((i == 0) ? 0 : lc[i - 1]) + ((j == 0) ? 0 : rc[j - 1]));
+                    sums.insert(sum);                        
+                }
+            }
+            uint_set::iterator it = sums.begin(), end = sums.end();
+            for (; it != end; ++it) {
+                oc.push_back(*it);
+            }            
+            std::sort(oc.begin(), oc.end());
+            DEBUG_CODE(                
+                for (unsigned i = 0; i + 1 < oc.size(); ++i) {
+                    SASSERT(oc[i] < oc[i+1]);
+                });
+            for (unsigned i = 0; i < oc.size(); ++i) {
+                sum2def.insert(oc[i], i);
+                trail.push_back(expr_ref_vector(m));
+            }
+            for (unsigned i = 0; i <= l.size(); ++i) {
+                for (unsigned j = (i == 0) ? 1 : 0; j <= r.size(); ++j) {
+                    if (i != 0 && j != 0 && (lc[i - 1] >= k || rc[j - 1] >= k)) continue;
+                    unsigned sum = std::min(k, ((i == 0) ? 0 : lc[i - 1]) + ((j == 0) ? 0 : rc[j - 1]));
+                    expr_ref_vector ands(m);
+                    if (i != 0) {
+                        ands.push_back(l[i - 1]);
+                    }
+                    if (j != 0) {
+                        ands.push_back(r[j - 1]);
+                    }
+                    trail[sum2def.find(sum)].push_back(::mk_and(ands));
+                }
+            }
+            for (unsigned i = 0; i < oc.size(); ++i) {
+                o.push_back(::mk_or(trail[sum2def.find(oc[i])]));
+            }
+        }
+
         /**
            \brief MiniSat+ based encoding of PB constraints. 
            The procedure is described in "Translating Pseudo-Boolean Constraints into SAT "
diff --git a/src/sat/sat_lookahead.h b/src/sat/sat_lookahead.h
index 3344e82e1..c4f6a4bba 100644
--- a/src/sat/sat_lookahead.h
+++ b/src/sat/sat_lookahead.h
@@ -282,8 +282,10 @@ namespace sat {
             inc_bstamp();
             set_bstamp(l);
             literal_vector const& conseq = m_binary[l.index()];
-            for (unsigned i = 0; i < conseq.size(); ++i) {
-                set_bstamp(conseq[i]);
+            literal_vector::const_iterator it = conseq.begin(); 
+            literal_vector::const_iterator end = conseq.end();
+            for (; it != end; ++it) {
+                set_bstamp(*it);
             }
         }
         bool is_stamped(literal l) const { return m_bstamp[l.index()] == m_bstamp_id; }
@@ -557,6 +559,7 @@ namespace sat {
             literal_vector::iterator it = m_binary[l.index()].begin(), end = m_binary[l.index()].end();
             for (; it != end; ++it) {
                 if (is_undef(*it)) sum += h[it->index()]; 
+                // if (m_freevars.contains(it->var())) sum += h[it->index()]; 
             }
             watch_list& wlist = m_watches[l.index()];
             watch_list::iterator wit = wlist.begin(), wend = wlist.end();
@@ -568,9 +571,8 @@ namespace sat {
                 case watched::TERNARY: {
                     literal l1 = wit->get_literal1();
                     literal l2 = wit->get_literal2();
-                    if (is_undef(l1) && is_undef(l2)) {
-                        tsum += h[l1.index()] * h[l2.index()]; 
-                    }
+                    // if (is_undef(l1) && is_undef(l2)) 
+                    tsum += h[l1.index()] * h[l2.index()]; 
                     break;
                 }
                 case watched::CLAUSE: {
@@ -1155,14 +1157,19 @@ namespace sat {
             // convert windfalls to binary clauses.
             if (!unsat) {
                 literal nlit = ~lit;
+
                 for (unsigned i = 0; i < m_wstack.size(); ++i) {
-                    ++m_stats.m_windfall_binaries;
                     literal l2 = m_wstack[i];
                     //update_prefix(~lit);
                     //update_prefix(m_wstack[i]);
                     TRACE("sat", tout << "windfall: " << nlit << " " << l2 << "\n";); 
+                    // if we use try_add_binary, then this may produce new assignments
+                    // these assignments get put on m_trail, and they are cleared by
+                    // reset_wnb. We would need to distinguish the trail that comes
+                    // from lookahead levels and the main search level for this to work.
                     add_binary(nlit, l2);
                 }
+                m_stats.m_windfall_binaries += m_wstack.size();
             }
             m_wstack.reset();
         }
@@ -1180,6 +1187,15 @@ namespace sat {
             return r;
         }
 
+        // 
+        // The current version is modeled after CDCL SAT solving data-structures.
+        // It borrows from the watch list data-structure. The cost tradeoffs are somewhat
+        // biased towards CDCL search overheads.
+        // If we walk over the positive occurrences of l, then those clauses can be retired so 
+        // that they don't interfere with calculation of H. Instead of removing clauses from the watch
+        // list one can swap them to the "back" and adjust a size indicator of the watch list
+        // Only the size indicator needs to be updated on backtracking.
+        // 
         void propagate_clauses(literal l) {
             SASSERT(is_true(l));
             if (inconsistent()) return;
@@ -1237,17 +1253,17 @@ namespace sat {
                     break;
                 }
                 case watched::CLAUSE: {
-                    clause_offset cls_off = it->get_clause_offset();
-                    clause & c = *(s.m_cls_allocator.get_clause(cls_off));
                     if (is_true(it->get_blocked_literal())) {
                         *it2 = *it;
                         ++it2;
                         break;
                     }
-
+                    clause_offset cls_off = it->get_clause_offset();
+                    clause & c = *(s.m_cls_allocator.get_clause(cls_off));
                     if (c[0] == ~l)
                         std::swap(c[0], c[1]);
                     if (is_true(c[0])) {
+                        it->set_blocked_literal(c[0]);
                         *it2 = *it;
                         it2++;
                         break;
@@ -1337,13 +1353,21 @@ namespace sat {
         }
 
         void propagate() {
-            for (; m_qhead < m_trail.size(); ++m_qhead) {
-                if (inconsistent()) break;
-                literal l = m_trail[m_qhead];
-                TRACE("sat", tout << "propagate " << l << " @ " << m_level << "\n";);
-                propagate_binary(l);
-                propagate_clauses(l);
+            while (!inconsistent() && m_qhead < m_trail.size()) {
+                unsigned i = m_qhead;
+                unsigned sz = m_trail.size();
+                for (; i < sz && !inconsistent(); ++i) {
+                    literal l = m_trail[i];
+                    TRACE("sat", tout << "propagate " << l << " @ " << m_level << "\n";);
+                    propagate_binary(l);
+                }
+                i = m_qhead;
+                for (; i < sz && !inconsistent(); ++i) {            
+                    propagate_clauses(m_trail[i]);
+                }
+                m_qhead = sz;
             }
+
             TRACE("sat_verbose", display(tout << scope_lvl() << " " << (inconsistent()?"unsat":"sat") << "\n"););
         }