diff --git a/src/math/polysat/boolean.cpp b/src/math/polysat/boolean.cpp
index 7a9e46a09..695460a18 100644
--- a/src/math/polysat/boolean.cpp
+++ b/src/math/polysat/boolean.cpp
@@ -40,7 +40,6 @@ namespace polysat {
             SASSERT_EQ(m_clause[var], nullptr);
             SASSERT_EQ(m_deps[var], null_dependency);
         }
-        m_free_vars.mk_var_eh(var);
         return var;
     }
 
@@ -72,6 +71,12 @@ namespace polysat {
         SASSERT(is_decision(lit));
     }
 
+    void bool_var_manager::decide(sat::literal lit, unsigned lvl) {
+        LOG("Decide literal " << lit << " @ " << lvl);
+        assign(kind_t::decision, lit, lvl, nullptr);
+        SASSERT(is_decision(lit));
+    }
+
     void bool_var_manager::eval(sat::literal lit, unsigned lvl) {
         LOG("Eval literal " << lit << " @ " << lvl);
         assign(kind_t::propagation, lit, lvl, nullptr);
diff --git a/src/math/polysat/boolean.h b/src/math/polysat/boolean.h
index 2ef826779..7a6b7edba 100644
--- a/src/math/polysat/boolean.h
+++ b/src/math/polysat/boolean.h
@@ -74,6 +74,7 @@ namespace polysat {
         unsigned_vector& activity() { return m_activity; }
         bool can_decide() const { return !m_free_vars.empty(); }
         sat::bool_var next_var() { return m_free_vars.next_var(); }
+        void track_var(sat::literal lit) { m_free_vars.mk_var_eh(lit.var()); }
 
         // TODO connect activity updates with solver
         void inc_activity(sat::literal lit) { m_activity[lit.var()]++; }
@@ -82,6 +83,8 @@ namespace polysat {
         /// Set the given literal to true
         void propagate(sat::literal lit, unsigned lvl, clause& reason);
         void decide(sat::literal lit, unsigned lvl, clause& lemma);
+        void decide(sat::literal lit, unsigned lvl);
+
         void eval(sat::literal lit, unsigned lvl);
         void asserted(sat::literal lit, unsigned lvl, dependency dep);
         void unassign(sat::literal lit);
diff --git a/src/math/polysat/solver.cpp b/src/math/polysat/solver.cpp
index d057d5a97..44583e735 100644
--- a/src/math/polysat/solver.cpp
+++ b/src/math/polysat/solver.cpp
@@ -150,20 +150,13 @@ namespace polysat {
         add_eq(b * q + r - a);
         add_noovfl(b, q);
         add_ule(r, b*q+r);
-        auto c1 = eq(b);
-        auto c2 = ult(r, b);
-        auto c3 = diseq(b);
-        auto c4 = eq(q + 1);
-        add_clause(c1, c2, false);
-        add_clause(c3, c4, false);
 
-        // BUG:
-        // need to watch these constraints.
-        // ... but activation discipline seems to 
-        // work only for lemmas. Literals are watched only when assigned true.
-        // The literals are de-activated
-        // after propagation
-        // Should these clauses then be added as lemmas that force a branch?
+        auto c_eq = eq(b);
+        add_clause(c_eq, ult(r, b), false);
+        add_clause(~c_eq, eq(q + 1), false);
+
+        // force decisions on whether b == 0
+        m_bvars.track_var(c_eq.blit());
 
         return std::tuple<pdd, pdd>(q, r);
     }
@@ -449,7 +442,10 @@ namespace polysat {
     void solver::decide() {
         LOG_H2("Decide");
         SASSERT(can_decide());
-        pdecide(m_free_pvars.next_var());
+        if (!m_free_pvars.empty()) 
+            pdecide(m_free_pvars.next_var());
+        else 
+            bdecide(m_bvars.next_var());
     }
 
     void solver::pdecide(pvar v) {
@@ -472,9 +468,16 @@ namespace polysat {
             push_level();
             assign_core(v, val, justification::decision(m_level));
             break;
-        }
+        }        
     }   
 
+    void solver::bdecide(sat::bool_var b) {
+        sat::literal lit(b);
+        m_bvars.decide(lit, m_level);
+        m_trail.push_back(trail_instr_t::assign_bool_i);
+        m_search.push_boolean(lit);
+    }
+
     void solver::assign_core(pvar v, rational const& val, justification const& j) {
         if (j.is_decision()) 
             ++m_stats.m_num_decisions;
@@ -766,16 +769,14 @@ namespace polysat {
         // The lemma where 'lit' comes from.
         // Currently, boolean decisions always come from guessing a literal of a learned non-unit lemma.
         clause* lemma = m_bvars.lemma(var);  // need to grab this while 'lit' is still assigned
-        // We only revert decisions that come from lemmas, so lemma must not be NULL here.
-        // (Externally asserted literals are at a base level, so we would return UNSAT instead of reverting.)
-        SASSERT(lemma);
 
         backjump(m_bvars.level(var) - 1);
 
         // reason should force ~lit after propagation
         add_clause(*reason);
 
-        enqueue_decision_on_lemma(*lemma);
+        if (lemma)
+            enqueue_decision_on_lemma(*lemma);
     }
 
     unsigned solver::level(sat::literal lit0, clause const& cl) {
diff --git a/src/math/polysat/solver.h b/src/math/polysat/solver.h
index c98feaf3c..88cb90914 100644
--- a/src/math/polysat/solver.h
+++ b/src/math/polysat/solver.h
@@ -185,7 +185,7 @@ namespace polysat {
         void set_conflict(clause& cl) { m_conflict.set(cl); }
         void set_conflict(pvar v) { m_conflict.set(v); }
 
-        bool can_decide() const { return !m_free_pvars.empty(); }
+        bool can_decide() const { return !m_free_pvars.empty() || m_bvars.can_decide(); }
         void decide();
         void pdecide(pvar v);
         void bdecide(sat::bool_var b);