diff --git a/src/math/lp/nra_solver.cpp b/src/math/lp/nra_solver.cpp
index 0f30272e9..98002d7cb 100644
--- a/src/math/lp/nra_solver.cpp
+++ b/src/math/lp/nra_solver.cpp
@@ -433,16 +433,26 @@ struct solver::imp {
         if (falsified.empty())
             return l_undef;
 
-        // Pick the falsified constraint with the smallest substitution
-        // expansion as a cheap LRA-side proxy for the lowest-degree
-        // heuristic that nlsat_solver::check(rvalues, clause) would apply.
+        // Pick the falsified constraint according to
+        // arith.nl.nra_check_assignment_pick:
+        //   0 - minimal substitution expansion (cheap LRA-side proxy
+        //       for the lowest-degree-in-max-var heuristic that
+        //       nlsat::solver::check(rvalues, clause) applies).
+        //   1 - uniformly random falsified constraint.
         lp::constraint_index best = falsified[0];
-        unsigned best_score = constraint_expansion_size(best);
-        for (unsigned k = 1; k < falsified.size(); ++k) {
-            unsigned sc = constraint_expansion_size(falsified[k]);
-            if (sc < best_score) {
-                best_score = sc;
-                best = falsified[k];
+        unsigned pick_mode = m_nla_core.params().arith_nl_nra_check_assignment_pick();
+        if (pick_mode == 1) {
+            unsigned k = m_nla_core.random() % falsified.size();
+            best = falsified[k];
+        }
+        else {
+            unsigned best_score = constraint_expansion_size(best);
+            for (unsigned k = 1; k < falsified.size(); ++k) {
+                unsigned sc = constraint_expansion_size(falsified[k]);
+                if (sc < best_score) {
+                    best_score = sc;
+                    best = falsified[k];
+                }
             }
         }
 
diff --git a/src/params/smt_params_helper.pyg b/src/params/smt_params_helper.pyg
index 6c8ce796d..204bc0e80 100644
--- a/src/params/smt_params_helper.pyg
+++ b/src/params/smt_params_helper.pyg
@@ -63,6 +63,7 @@ def_module_params(module_name='smt',
                           ('arith.nl.nra', BOOL, True, 'call nra_solver when incremental linearization does not produce a lemma, this option is ignored when arith.nl=false, relevant only if smt.arith.solver=6'),
                           ('arith.nl.nra_check_assignment', BOOL, True, 'call check_assignment in nra_solver to verify current assignment against nlsat constraints'),
                           ('arith.nl.nra_check_assignment_max_fail', UINT, 7, 'maximum consecutive check_assignment failures before disabling it'),
+                          ('arith.nl.nra_check_assignment_pick', UINT, 0, 'falsified-literal selection in check_assignment: 0 - minimal degree (size) of the max variable (default), 1 - random'),
                           ('arith.nl.branching', BOOL, True, 'branching on integer variables in non linear clusters'),
                           ('arith.nl.expensive_patching', BOOL, False, 'use the expensive of monomials'),
                           ('arith.nl.rounds', UINT, 1024, 'threshold for number of (nested) final checks for non linear arithmetic, relevant only if smt.arith.solver=2'),