diff --git a/src/opt/maxcore.cpp b/src/opt/maxcore.cpp
index 499d0f65e..ab2129e27 100644
--- a/src/opt/maxcore.cpp
+++ b/src/opt/maxcore.cpp
@@ -81,7 +81,8 @@ using namespace opt;
 class maxcore : public maxsmt_solver_base {
 public:
     enum strategy_t {
-        s_primal,
+        s_primal, 
+        s_primalw,
         s_primal_dual,
         s_primal_binary,
         s_rc2,
@@ -155,6 +156,9 @@ public:
         case s_primal:
             m_trace_id = "maxres";
             break;
+        case s_primalw:
+            m_trace_id = "maxresw";
+            break;
         case s_primal_dual:
             m_trace_id = "pd-maxres";
             break;
@@ -371,6 +375,7 @@ public:
         m_defs.reset();
         switch(m_st) {
         case s_primal:
+        case s_primalw:
         case s_primal_binary:
         case s_rc2:
         case s_primal_binary_rc2:
@@ -503,6 +508,9 @@ public:
         if (m_enable_core_rotate)
             return core_rotate();
 
+        if (m_st == s_primalw) 
+            return process_unsatw();        
+
         vector<weighted_core> cores;
         lbool is_sat = get_cores(cores);
         if (is_sat != l_true) {
@@ -517,6 +525,114 @@ public:
         }
     }
 
+    lbool process_unsatw() {
+        vector<weighted_softs> cores;
+        lbool is_sat = get_cores(cores);
+        if (is_sat != l_true) {
+            return is_sat;
+        }
+        if (cores.empty()) {
+            return l_false;
+        }
+        else {
+            for (auto const &core : cores) {
+                for (unsigned i = 0; i + 1 < core.size(); ++i) {
+                    auto [f, def, w] = core[i];
+                    add(def);
+                    new_assumption(f, w);             
+                }
+                auto [f, def, w] = core.back();
+                add(def);
+                f = mk_not(f);
+                add(f);
+                m_lower += w;
+                trace();
+            }
+            return l_true;
+        }
+    }
+
+    lbool get_cores(vector<weighted_softs>& cores) {
+        lbool is_sat = l_false;
+        cores.reset();
+        exprs core;
+        while (is_sat == l_false) {
+            core.reset();
+            expr_ref_vector _core(m);
+            s().get_unsat_core(_core);
+            model_ref mdl;
+            get_mus_model(mdl);
+            is_sat = minimize_core(_core);
+            core.append(_core.size(), _core.data());
+            DEBUG_CODE(verify_core(core););
+            ++m_stats.m_num_cores;
+            if (is_sat != l_true) {
+                IF_VERBOSE(100, verbose_stream() << "(opt.maxresw minimization failed)\n";);
+                break;
+            }
+            if (core.empty()) {
+                IF_VERBOSE(100, verbose_stream() << "(opt.maxresw core is empty)\n";);
+                TRACE(opt, tout << "empty core\n";);
+                cores.reset();
+                m_lower = m_upper;
+                return l_true;
+            }
+
+            weighted_softs soft;
+            for (expr* e : core) {
+                rational w = get_weight(e);
+                expr_ref fml(m.mk_true(), m);
+                expr_ref s(e, m);
+                soft.push_back({s, fml, w});
+            }
+            std::sort(soft.begin(), soft.end(),
+                      [](auto const& a, auto const& b) {
+                          return a.weight > b.weight;
+                      });
+            remove_soft(core, m_asms);
+            expr_ref fml(m), d(m);
+            for (unsigned i = 0; i + 1 < soft.size(); ++i) {
+                rational w1 = soft[i].weight;
+                rational w2 = soft[i + 1].weight;
+                auto s1 = soft[i].soft;
+                auto s2 = soft[i + 1].soft;
+                // verbose_stream() << "processing softs of weights " << s1 << " " << w1 << " and " << s2 << " " << w2 << "\n";
+                SASSERT(w1 >= w2);
+                // s1 := s1 or s2
+                // d  => s1 & s2
+                // s2 := d
+                // assume s1, w1 - w2
+                // new soft constraints are s1 or s2 : w2, s1 & s2 or s3 : w3, ...
+                // remove soft constraint of weight w_n
+                d = mk_fresh_bool("d");
+                fml = m.mk_and(s1, s2);
+                update_model(d, fml);
+                soft[i].weight = w2;
+                soft[i].soft = m.mk_or(s1, s2);
+                soft[i + 1].soft = d;
+                soft[i + 1].def = m.mk_implies(d, fml);
+                if (w1 > w2) { 
+                    for (unsigned j = 0; j < i; ++j) {
+                        auto [s, def, w] = soft[j];
+                        if (!m.is_true(def)) {
+                            add(def);
+                            soft[j].def = m.mk_true();
+                        }
+                    }
+                    new_assumption(s1, w1 - w2);
+                }
+            }
+            cores.push_back(soft);
+
+            if (core.size() >= m_max_core_size)
+                break;
+
+            is_sat = check_sat_hill_climb(m_asms);
+        }
+
+        return is_sat;
+    }
+
     lbool core_rotate() {
         cores find_cores(s(), m_lnsctx);
         find_cores.updt_params(m_params);
@@ -570,6 +686,8 @@ public:
         case strategy_t::s_primal_binary_rc2:
             max_resolve_rc2bin(core, w);
             break;
+        case strategy_t::s_primalw: 
+            UNREACHABLE();
         default:
             max_resolve(core, w);
             break;
@@ -637,17 +755,22 @@ public:
 
     rational split_core(exprs const& core) {
         rational w = core_weight(core);
-        // add fresh soft clauses for weights that are above w.
+        // add fresh soft clauses for weights that are above w.     
         for (expr* e : core) {
             rational w2 = get_weight(e);
             if (w2 > w) {
                 rational w3 = w2 - w;
-                new_assumption(e, w3);
+                new_assumption(e, w3);               
             }
         }
         return w;
     }
 
+    // (c1, w1), ... , (cn, wn), w1 <= w2 <= ... <= wn
+    // clones are (c2, w2 - w1), (c3, w3 - w2), ... , (cn, wn - w_{n-1})
+    // soft constraints are
+    // (c1 or c2, w1), (c1 & c2 or c3, w2), ..., (c1 & ... & c_{n-1} or c_n, w_{n-1})
+
     void display_vec(std::ostream& out, exprs const& exprs) {
         display_vec(out, exprs.size(), exprs.data());
     }
@@ -1129,6 +1252,10 @@ opt::maxsmt_solver_base* opt::mk_maxres(
     return alloc(maxcore, c, id, soft, maxcore::s_primal);
 }
 
+opt::maxsmt_solver_base *opt::mk_maxresw(maxsat_context &c, unsigned id, vector<soft> &soft) {
+    return alloc(maxcore, c, id, soft, maxcore::s_primalw);
+}
+
 opt::maxsmt_solver_base* opt::mk_rc2(
     maxsat_context& c, unsigned id, vector<soft>& soft) {
     return alloc(maxcore, c, id, soft, maxcore::s_rc2);
diff --git a/src/opt/maxcore.h b/src/opt/maxcore.h
index 2038c5e98..283fee850 100644
--- a/src/opt/maxcore.h
+++ b/src/opt/maxcore.h
@@ -27,6 +27,8 @@ namespace opt {
 
     maxsmt_solver_base* mk_maxres(maxsat_context& c, unsigned id, vector<soft>& soft);
 
+    maxsmt_solver_base *mk_maxresw(maxsat_context &c, unsigned id, vector<soft> &soft);
+
     maxsmt_solver_base* mk_maxres_binary(maxsat_context& c, unsigned id, vector<soft>& soft);
 
     maxsmt_solver_base* mk_primal_dual_maxres(maxsat_context& c, unsigned id, vector<soft>& soft);
diff --git a/src/opt/maxsmt.cpp b/src/opt/maxsmt.cpp
index f6b083ecf..d1d150671 100644
--- a/src/opt/maxsmt.cpp
+++ b/src/opt/maxsmt.cpp
@@ -187,6 +187,8 @@ namespace opt {
         TRACE(opt_verbose, s().display(tout << "maxsmt\n") << "\n";);
         if (!committed && optp.maxlex_enable() && is_maxlex(m_soft)) 
             m_msolver = mk_maxlex(m_c, m_index, m_soft);            
+        else if (maxsat_engine == symbol("maxresw"))
+            m_msolver = mk_maxresw(m_c, m_index, m_soft);
         else if (m_soft.empty() || maxsat_engine == symbol("maxres") || maxsat_engine == symbol::null)             
             m_msolver = mk_maxres(m_c, m_index, m_soft);            
         else if (maxsat_engine == symbol("maxres-bin"))             
diff --git a/src/opt/maxsmt.h b/src/opt/maxsmt.h
index 17306b222..185bd2aca 100644
--- a/src/opt/maxsmt.h
+++ b/src/opt/maxsmt.h
@@ -38,6 +38,14 @@ namespace opt {
             m_core(c), m_weight(w) {}
     };
 
+    struct weighted_soft {
+        expr_ref  soft;
+        expr_ref  def;
+        rational  weight;
+        weighted_soft(expr_ref const& s, expr_ref const& d, rational const& w): soft(s), def(d), weight(w) {}
+    };
+    using weighted_softs = vector<weighted_soft>;
+
     class maxsat_context;
 
     class maxsmt_solver {
diff --git a/src/opt/opt_params.pyg b/src/opt/opt_params.pyg
index 15f5e5d05..7960a8a42 100644
--- a/src/opt/opt_params.pyg
+++ b/src/opt/opt_params.pyg
@@ -2,7 +2,7 @@ def_module_params('opt',
                   description='optimization parameters',
                   export=True,
                   params=(('optsmt_engine', SYMBOL, 'basic', "select optimization engine: 'basic', 'symba'"),
-                          ('maxsat_engine', SYMBOL, 'maxres', "select engine for maxsat: 'core_maxsat', 'wmax', 'maxres', 'pd-maxres', 'maxres-bin', 'rc2'"),
+                          ('maxsat_engine', SYMBOL, 'maxres', "select engine for maxsat: 'core_maxsat', 'wmax', 'maxres', 'maxresw', 'pd-maxres', 'maxres-bin', 'rc2'"),
                           ('priority', SYMBOL, 'lex', "select how to prioritize objectives: 'lex' (lexicographic), 'pareto', 'box'"),
                           ('dump_benchmarks', BOOL, False, 'dump benchmarks for profiling'),
                           ('dump_models', BOOL, False, 'display intermediary models to stdout'),
diff --git a/src/opt/opt_parse.cpp b/src/opt/opt_parse.cpp
index 159246281..6b0dbb66a 100644
--- a/src/opt/opt_parse.cpp
+++ b/src/opt/opt_parse.cpp
@@ -137,6 +137,25 @@ class wcnf {
         result = to_app(mk_or(m, ors.size(), ors.data()));
         return result;
     }
+
+    app_ref read_hard_clause() {
+        int parsed_lit;
+        int var;
+        app_ref result(m), p(m);
+        expr_ref_vector ors(m);
+        while (true) {
+            parsed_lit = in.parse_int();
+            if (parsed_lit == 0)
+                break;
+            var = abs(parsed_lit);
+            p = m.mk_const(symbol((unsigned)var), m.mk_bool_sort());
+            if (parsed_lit < 0)
+                p = m.mk_not(p);
+            ors.push_back(p);
+        }
+        result = to_app(mk_or(m, ors.size(), ors.data()));
+        return result;
+    }
     
     void parse_spec(unsigned& num_vars, unsigned& num_clauses, unsigned& max_weight) {
         in.parse_token("wcnf");
@@ -152,7 +171,7 @@ public:
     }
     
     void parse() {
-        unsigned num_vars = 0, num_clauses = 0, max_weight = 0;
+        unsigned num_vars = 0, num_clauses = 0, max_weight = UINT_MAX;
         while (true) {
             in.skip_whitespace();
             if (in.eof()) {
@@ -165,6 +184,11 @@ public:
                 ++in;
                 parse_spec(num_vars, num_clauses, max_weight);
             }
+            else if (*in == 'h') {
+                in.next();                
+                app_ref cls = read_hard_clause();
+                opt.add_hard_constraint(cls);
+            }
             else {
                 unsigned weight = 0;
                 app_ref cls = read_clause(weight);