diff --git a/src/params/smt_parallel_params.pyg b/src/params/smt_parallel_params.pyg
index 89891deb1..cfb5f276f 100644
--- a/src/params/smt_parallel_params.pyg
+++ b/src/params/smt_parallel_params.pyg
@@ -5,5 +5,5 @@ def_module_params('smt_parallel',
                         ('share_units', BOOL, True, 'share units'),
                         ('share_conflicts', BOOL, True, 'share conflicts'),
                         ('never_cube', BOOL, False, 'never cube'),
-                        ('only_eager_cube', BOOL, False, 'only eager cube'),
+                        ('frugal_cube_only', BOOL, False, 'only apply frugal cube strategy'),
               ))
diff --git a/src/smt/smt_parallel.cpp b/src/smt/smt_parallel.cpp
index 9bbf704d2..86f9d5a21 100644
--- a/src/smt/smt_parallel.cpp
+++ b/src/smt/smt_parallel.cpp
@@ -362,7 +362,7 @@ namespace smt {
 
         std::scoped_lock lock(mux);
         unsigned max_cubes = 1000;
-        bool greedy_mode = (m_cubes.size() <= max_cubes);
+        bool greedy_mode = (m_cubes.size() <= max_cubes) && !smt_parallel_params(p.ctx.m_params).frugal_cube_only();
         unsigned a_worker_start_idx = 0;
 
         //