diff --git a/src/sat/ba_solver.cpp b/src/sat/ba_solver.cpp
index eedca9ce9..e77e1172d 100644
--- a/src/sat/ba_solver.cpp
+++ b/src/sat/ba_solver.cpp
@@ -1739,6 +1739,25 @@ namespace sat {
         SASSERT(validate_unit_propagation(p, r, l));
     }
 
+    bool ba_solver::is_extended_binary(ext_justification_idx idx, literal_vector & r) {
+        constraint const& c = index2constraint(idx);
+        switch (c.tag()) {
+        case card_t: {
+            card const& ca = c.to_card();
+            if (ca.size() == ca.k() + 1 && ca.lit() == null_literal) {
+                r.reset();
+                for (literal l : ca) r.push_back(l);
+                return true;
+            }
+            else {
+                return false;
+            }
+        }
+        default:
+            return false;
+        }
+    }
+
     void ba_solver::simplify(xor& x) {
         // no-op
     }
@@ -2004,17 +2023,39 @@ namespace sat {
     /**
        \brief Lex on (glue, size)
     */
-    struct constraint_glue_lt {
+    struct constraint_glue_psm_lt {
         bool operator()(ba_solver::constraint const * c1, ba_solver::constraint const * c2) const {
             return 
                 (c1->glue()  < c2->glue()) ||
-                (c1->glue() == c2->glue() && c1->size() < c2->size());
+                (c1->glue() == c2->glue() && 
+                 (c1->psm() < c2->psm() || 
+                  (c1->psm() == c2->psm() && c1->size() < c2->size())));
         }
     };
 
+    void ba_solver::update_psm(constraint& c) const {
+        unsigned r = 0;
+        switch (c.tag()) {            
+        case card_t: 
+            for (literal l : c.to_card()) {                
+                if (s().m_phase[l.var()] == (l.sign() ? NEG_PHASE : POS_PHASE)) ++r;
+            }
+            break;
+        case pb_t:
+            for (wliteral l : c.to_pb()) {                
+                if (s().m_phase[l.second.var()] == (l.second.sign() ? NEG_PHASE : POS_PHASE)) ++r;
+            }
+            break;
+        default:
+            break;
+        }
+        c.set_psm(r);
+    }
+
     void ba_solver::gc() {
-        std::stable_sort(m_learned.begin(), m_learned.end(), constraint_glue_lt());
-        gc_half("glue");
+        for (auto & c : m_learned) update_psm(*c);
+        std::stable_sort(m_learned.begin(), m_learned.end(), constraint_glue_psm_lt());
+        gc_half("glue-psm");
         cleanup_constraints(m_learned, true);
     }
 
diff --git a/src/sat/ba_solver.h b/src/sat/ba_solver.h
index 2169f5845..5347cac22 100644
--- a/src/sat/ba_solver.h
+++ b/src/sat/ba_solver.h
@@ -62,12 +62,13 @@ namespace sat {
             bool           m_removed;
             literal        m_lit;
             unsigned       m_glue;
+            unsigned       m_psm;
             unsigned       m_size;
             size_t         m_obj_size;
             bool           m_learned;
             unsigned       m_id;
         public:
-            constraint(tag_t t, unsigned id, literal l, unsigned sz, size_t osz): m_tag(t), m_removed(false), m_lit(l), m_glue(0), m_size(sz), m_obj_size(osz), m_learned(false), m_id(id) {}
+            constraint(tag_t t, unsigned id, literal l, unsigned sz, size_t osz): m_tag(t), m_removed(false), m_lit(l), m_glue(0), m_psm(0), m_size(sz), m_obj_size(osz), m_learned(false), m_id(id) {}
             ext_constraint_idx index() const { return reinterpret_cast<ext_constraint_idx>(this); }
             unsigned id() const { return m_id; }
             tag_t tag() const { return m_tag; }
@@ -79,7 +80,9 @@ namespace sat {
             void remove() { m_removed = true; }
             void nullify_literal() { m_lit = null_literal; }
             unsigned glue() const { return m_glue; }
-            void set_glue(unsigned g) { m_glue = g; }            
+            void set_glue(unsigned g) { m_glue = g; }          
+            unsigned psm() const { return m_psm; }
+            void set_psm(unsigned p) { m_psm = p; }
             void set_learned(bool f) { m_learned = f; }
             bool learned() const { return m_learned; }            
 
@@ -265,6 +268,7 @@ namespace sat {
         void subsumption(constraint& c1);
         void subsumption(card& c1);
         void gc_half(char const* _method);
+        void update_psm(constraint& c) const;
         void mutex_reduction();
 
         typedef vector<std::pair<rational, lp::var_index>> lhs_t;
@@ -442,6 +446,7 @@ namespace sat {
         virtual void pop_reinit();
         virtual void gc(); 
         virtual double get_reward(literal l, ext_justification_idx idx, literal_occs_fun& occs) const;
+        virtual bool is_extended_binary(ext_justification_idx idx, literal_vector & r);
 
         ptr_vector<constraint> const & constraints() const { return m_constraints; }
 
diff --git a/src/sat/sat_extension.h b/src/sat/sat_extension.h
index 87f1904ed..406cc6421 100644
--- a/src/sat/sat_extension.h
+++ b/src/sat/sat_extension.h
@@ -43,6 +43,7 @@ namespace sat {
         virtual bool propagate(literal l, ext_constraint_idx idx) = 0;
         virtual double get_reward(literal l, ext_constraint_idx idx, literal_occs_fun& occs) const = 0;
         virtual void get_antecedents(literal l, ext_justification_idx idx, literal_vector & r) = 0;
+        virtual bool is_extended_binary(ext_justification_idx idx, literal_vector & r) = 0;
         virtual void asserted(literal l) = 0;
         virtual check_result check() = 0;
         virtual lbool resolve_conflict() { return l_undef; } // stores result in sat::solver::m_lemma
diff --git a/src/sat/sat_lookahead.cpp b/src/sat/sat_lookahead.cpp
index b5229dc54..aaf392ae3 100644
--- a/src/sat/sat_lookahead.cpp
+++ b/src/sat/sat_lookahead.cpp
@@ -503,6 +503,7 @@ namespace sat {
     // arcs are added in the opposite direction of implications.
     // So for implications l => u we add arcs u -> l
     void lookahead::init_arcs(literal l) {
+        literal_vector lits;
         literal_vector const& succ = m_binary[l.index()];
         for (unsigned i = 0; i < succ.size(); ++i) {
             literal u = succ[i];
@@ -512,6 +513,16 @@ namespace sat {
                 add_arc( u,  l);
             }
         }
+        for (auto w : m_watches[l.index()]) {
+            if (w.is_ext_constraint() && m_s.m_ext->is_extended_binary(w.get_ext_constraint_idx(), lits)) {
+                for (literal u : lits) {
+                    if (u.index() > l.index() && is_stamped(u)) {
+                        add_arc(~l, ~u);
+                        add_arc( u,  l);
+                    }
+                }
+            }
+        }
     }
 
     void lookahead::get_scc(literal v) {
diff --git a/src/sat/sat_scc.cpp b/src/sat/sat_scc.cpp
index ec77ebfbd..15108c7fd 100644
--- a/src/sat/sat_scc.cpp
+++ b/src/sat/sat_scc.cpp
@@ -33,10 +33,11 @@ namespace sat {
 
     struct frame {
         unsigned  m_lidx;
+        unsigned  m_succ_idx;
         bool      m_first;
         watched * m_it;
         watched * m_end;
-        frame(unsigned lidx, watched * it, watched * end):m_lidx(lidx), m_first(true), m_it(it), m_end(end) {}
+        frame(unsigned lidx, watched * it, watched * end, unsigned sidx = 0):m_lidx(lidx), m_succ_idx(sidx), m_first(true), m_it(it), m_end(end) {}
     };
     typedef svector<frame> frames;
 
@@ -75,7 +76,7 @@ namespace sat {
         index.resize(num_lits, UINT_MAX);
         lowlink.resize(num_lits, UINT_MAX);
         in_s.resize(num_lits, false);
-        literal_vector roots;
+        literal_vector roots, lits;
         roots.resize(m_solver.num_vars(), null_literal);
         unsigned next_index = 0;
         svector<frame>   frames;
@@ -106,6 +107,7 @@ namespace sat {
                 frame & fr = frames.back();
                 unsigned l_idx = fr.m_lidx;
                 if (!fr.m_first) {
+                    SASSERT(fr.m_it->is_binary_clause());
                     // after visiting child
                     literal l2 = fr.m_it->get_literal();
                     unsigned l2_idx = l2.index();