diff --git a/src/opt/CMakeLists.txt b/src/opt/CMakeLists.txt
index c652bcaea41..c815ae08eba 100644
--- a/src/opt/CMakeLists.txt
+++ b/src/opt/CMakeLists.txt
@@ -1,7 +1,7 @@
 z3_add_component(opt
   SOURCES
+    maxcore.cpp
     maxlex.cpp
-    maxres.cpp
     maxsmt.cpp
     opt_cmds.cpp
     opt_context.cpp
diff --git a/src/opt/maxres.cpp b/src/opt/maxcore.cpp
similarity index 91%
rename from src/opt/maxres.cpp
rename to src/opt/maxcore.cpp
index c4639c726dd..4369b10faef 100644
--- a/src/opt/maxres.cpp
+++ b/src/opt/maxcore.cpp
@@ -3,14 +3,17 @@ Copyright (c) 2014 Microsoft Corporation
 
 Module Name:
 
-    maxsres.cpp
+    maxcore.cpp
 
 Abstract:
    
-    MaxRes (weighted) max-sat algorithms:
+    Core based (weighted) max-sat algorithms:
+
+    - mu:        max-sat algorithm by Nina and Bacchus, AAAI 2014.
+    - mus-mss:   based on dual refinement of bounds.
+    - binary
+    - binary-delay
 
-    - mus:     max-sat algorithm by Nina and Bacchus, AAAI 2014.
-    - mus-mss: based on dual refinement of bounds.
 
     MaxRes is a core-guided approach to maxsat.
     MusMssMaxRes extends the core-guided approach by
@@ -64,17 +67,18 @@ Module Name:
 #include "opt/opt_params.hpp"
 #include "opt/opt_lns.h"
 #include "opt/maxsmt.h"
-#include "opt/maxres.h"
+#include "opt/maxcore.h"
 
 using namespace opt;
 
-class maxres : public maxsmt_solver_base {
+class maxcore : public maxsmt_solver_base {
 public:
     enum strategy_t {
         s_primal,
         s_primal_dual,
         s_primal_binary,
-        s_primal_binary_delay
+        s_primal_binary_delay,
+        s_rc2        
     };
 private:
     struct stats {
@@ -86,10 +90,10 @@ class maxres : public maxsmt_solver_base {
         }
     };
 
-    struct lns_maxres : public lns_context {
-        maxres& i;
-        lns_maxres(maxres& i) :i(i) {}
-        ~lns_maxres() override {}
+    struct lns_maxcore : public lns_context {
+        maxcore& i;
+        lns_maxcore(maxcore& i) :i(i) {}
+        ~lns_maxcore() override {}
         void update_model(model_ref& mdl) override { i.update_assignment(mdl); }
         void relax_cores(vector<expr_ref_vector> const& cores) override { i.relax_cores(cores); }
         rational cost(model& mdl) override { return i.cost(mdl); }
@@ -108,7 +112,7 @@ class maxres : public maxsmt_solver_base {
     strategy_t       m_st;
     rational         m_max_upper;    
     model_ref        m_csmodel;
-    lns_maxres       m_lnsctx;
+    lns_maxcore      m_lnsctx;
     lns              m_lns;
     unsigned         m_correction_set_size;
     bool             m_found_feasible_optimum;
@@ -130,7 +134,7 @@ class maxres : public maxsmt_solver_base {
     typedef ptr_vector<expr> exprs;
 
 public:
-    maxres(maxsat_context& c, unsigned index,
+    maxcore(maxsat_context& c, unsigned index,
            vector<soft>& soft,
            strategy_t st):
         maxsmt_solver_base(c, soft, index),
@@ -168,7 +172,7 @@ class maxres : public maxsmt_solver_base {
         }        
     }
 
-    ~maxres() override {}
+    ~maxcore() override {}
 
     bool is_literal(expr* l) {
         return 
@@ -375,8 +379,8 @@ class maxres : public maxsmt_solver_base {
     }
 
     void collect_statistics(statistics& st) const override {
-        st.update("maxres-cores", m_stats.m_num_cores);
-        st.update("maxres-correction-sets", m_stats.m_num_cs);
+        st.update("maxsat-cores", m_stats.m_num_cores);
+        st.update("maxsat-correction-sets", m_stats.m_num_cs);
     }
 
     struct weighted_core {
@@ -456,8 +460,8 @@ class maxres : public maxsmt_solver_base {
     }
 
     struct compare_asm {
-        maxres& mr;
-        compare_asm(maxres& mr):mr(mr) {}
+        maxcore& mr;
+        compare_asm(maxcore& mr):mr(mr) {}
         bool operator()(expr* a, expr* b) const {
             rational w1 = mr.get_weight(a);
             rational w2 = mr.get_weight(b);
@@ -550,6 +554,9 @@ class maxres : public maxsmt_solver_base {
         case strategy_t::s_primal_binary_delay:
             bin_delay_max_resolve(core, w);
             break;
+        case strategy_t::s_rc2:
+            max_resolve_rc2(core, w);
+            break;
         default:
             max_resolve(core, w);
             break;
@@ -747,6 +754,7 @@ class maxres : public maxsmt_solver_base {
     }
 
 
+    // binary - with delayed unfolding of new soft clauses.
     struct unfold_record {
         ptr_vector<expr> ws;
         rational weight;
@@ -823,6 +831,63 @@ class maxres : public maxsmt_solver_base {
         s().assert_expr(m.mk_not(core.back()));
     }
 
+    // rc2, using cardinality constraints
+
+    // create and cache at-most k constraints
+    struct bound_info {
+        ptr_vector<expr> es;
+        unsigned         k = 0;
+        rational         weight;
+        bound_info() {}
+        bound_info(ptr_vector<expr> const& es, unsigned k, rational const& weight):
+            es(es), k(k), weight(weight) {}
+        bound_info(expr_ref_vector const& es, unsigned k, rational const& weight):
+            es(es.size(), es.data()), k(k), weight(weight) {}
+    };
+    
+    obj_map<expr, expr*>      m_at_mostk;
+    obj_map<expr, bound_info> m_bounds;
+
+    expr* mk_atmost(expr_ref_vector const& es, unsigned bound, rational const& weight) {
+        pb_util pb(m);
+        expr_ref am(pb.mk_at_most_k(es, bound), m);
+        expr* r = nullptr;
+        if (m_at_mostk.find(am, r))
+            return r;
+        r = mk_fresh_bool("r");
+        m_trail.push_back(am);
+        bound_info b(es, bound, weight);
+        m_at_mostk.insert(am, r);
+        m_bounds.insert(r, b);
+        expr_ref fml(m);
+        fml = m.mk_implies(r, am);
+        add(fml);
+        m_defs.push_back(fml);
+        update_model(r, am);
+        return r;
+    }
+
+    void max_resolve_rc2(exprs const& core, rational weight) {
+        expr_ref_vector ncore(m);
+        for (expr* f : core) {
+            bound_info b;
+            if (!m_bounds.find(f, b))
+                continue;
+            m_bounds.remove(f);
+            if (b.k + 1 >= b.es.size())
+                continue;
+            expr_ref_vector es(m, b.es.size(), b.es.data());
+            expr* amk = mk_atmost(es, b.k + 1, b.weight);
+            new_assumption(amk, b.weight);
+            ncore.push_back(mk_not(m, f));
+            m_unfold_upper -= b.weight;
+        }
+        m_unfold_upper += rational(core.size() - 1) * weight;
+        expr* am = mk_atmost(ncore, 1, weight);
+        new_assumption(am, weight);
+    }
+    
+
     // cs is a correction set (a complement of a (maximal) satisfying assignment).
     void cs_max_resolve(exprs const& cs, rational const& w) {
         if (cs.empty()) return;
@@ -1009,6 +1074,8 @@ class maxres : public maxsmt_solver_base {
         m_correction_set_size = 0;
         m_unfold.reset();
         m_unfold_upper = 0;
+        m_at_mostk.reset();
+        m_bounds.reset();
         return l_true;
     }
 
@@ -1016,8 +1083,7 @@ class maxres : public maxsmt_solver_base {
         if (m_found_feasible_optimum) {
             add(m_defs);
             add(m_asms);
-            TRACE("opt", tout << "Committing feasible solution\ndefs:" << m_defs << "\nasms:" << m_asms << "\n";);
-
+            TRACE("opt", tout << "Committing feasible solution\ndefs:" << m_defs << "\nasms:" << m_asms << "\n");
         }
         // else: there is only a single assignment to these soft constraints.
     }
@@ -1071,21 +1137,27 @@ class maxres : public maxsmt_solver_base {
 
 opt::maxsmt_solver_base* opt::mk_maxres(
     maxsat_context& c, unsigned id, vector<soft>& soft) {
-    return alloc(maxres, c, id, soft, maxres::s_primal);
+    return alloc(maxcore, c, id, soft, maxcore::s_primal);
+}
+
+opt::maxsmt_solver_base* opt::mk_rc2(
+    maxsat_context& c, unsigned id, vector<soft>& soft) {
+    return alloc(maxcore, c, id, soft, maxcore::s_rc2);
 }
 
 opt::maxsmt_solver_base* opt::mk_maxres_binary(
     maxsat_context& c, unsigned id, vector<soft>& soft) {
-    return alloc(maxres, c, id, soft, maxres::s_primal_binary);
+    return alloc(maxcore, c, id, soft, maxcore::s_primal_binary);
 }
 
 opt::maxsmt_solver_base* opt::mk_maxres_binary_delay(
     maxsat_context& c, unsigned id, vector<soft>& soft) {
-    return alloc(maxres, c, id, soft, maxres::s_primal_binary_delay);
+    return alloc(maxcore, c, id, soft, maxcore::s_primal_binary_delay);
 }
 
 opt::maxsmt_solver_base* opt::mk_primal_dual_maxres(
     maxsat_context& c, unsigned id, vector<soft>& soft) {
-    return alloc(maxres, c, id, soft, maxres::s_primal_dual);
+    return alloc(maxcore, c, id, soft, maxcore::s_primal_dual);
 }
 
+
diff --git a/src/opt/maxres.h b/src/opt/maxcore.h
similarity index 78%
rename from src/opt/maxres.h
rename to src/opt/maxcore.h
index 947b60492a6..42efeb0bf95 100644
--- a/src/opt/maxres.h
+++ b/src/opt/maxcore.h
@@ -7,7 +7,7 @@ Module Name:
 
 Abstract:
    
-    MaxRes (weighted) max-sat algorithm by Nina and Bacchus, AAAI 2014.
+    Maxcore (weighted) max-sat algorithm by Nina and Bacchus, AAAI 2014.
 
 Author:
 
@@ -21,6 +21,8 @@ Module Name:
 
 namespace opt {
 
+    maxsmt_solver_base* mk_rc2(maxsat_context& c, unsigned id, vector<soft>& soft);
+
     maxsmt_solver_base* mk_maxres(maxsat_context& c, unsigned id, vector<soft>& soft);
 
     maxsmt_solver_base* mk_maxres_binary(maxsat_context& c, unsigned id, vector<soft>& soft);
diff --git a/src/opt/maxsmt.cpp b/src/opt/maxsmt.cpp
index f346a898003..b2cdedf6442 100644
--- a/src/opt/maxsmt.cpp
+++ b/src/opt/maxsmt.cpp
@@ -23,7 +23,7 @@ Module Name:
 #include "ast/ast_util.h"
 #include "ast/pb_decl_plugin.h"
 #include "opt/maxsmt.h"
-#include "opt/maxres.h"
+#include "opt/maxcore.h"
 #include "opt/maxlex.h"
 #include "opt/wmax.h"
 #include "opt/opt_params.hpp"
@@ -194,6 +194,9 @@ namespace opt {
         else if (maxsat_engine == symbol("maxres-bin")) {            
             m_msolver = mk_maxres_binary(m_c, m_index, m_soft);
         }
+        else if (maxsat_engine == symbol("rc2")) {            
+            m_msolver = mk_rc2(m_c, m_index, m_soft);
+        }
         else if (maxsat_engine == symbol("maxres-bin-delay")) {            
             m_msolver = mk_maxres_binary_delay(m_c, m_index, m_soft);
         }
diff --git a/src/opt/opt_params.pyg b/src/opt/opt_params.pyg
index cb8f1d1295a..914b3a72ba3 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', 'maxres-bin-delay'"),
+                          ('maxsat_engine', SYMBOL, 'maxres', "select engine for maxsat: 'core_maxsat', 'wmax', 'maxres', 'pd-maxres', 'maxres-bin', 'maxres-bin-delay', 'rc2'"),
                           ('priority', SYMBOL, 'lex', "select how to priortize objectives: 'lex' (lexicographic), 'pareto', 'box'"),
                           ('dump_benchmarks', BOOL, False, 'dump benchmarks for profiling'),
                           ('dump_models', BOOL, False, 'display intermediary models to stdout'),