diff --git a/pyomo/contrib/mindtpy/tests/test_mindtpy_feas_pump.py b/pyomo/contrib/mindtpy/tests/test_mindtpy_feas_pump.py
index 697a63d17c8..dcb5c4bce75 100644
--- a/pyomo/contrib/mindtpy/tests/test_mindtpy_feas_pump.py
+++ b/pyomo/contrib/mindtpy/tests/test_mindtpy_feas_pump.py
@@ -17,7 +17,7 @@
 from pyomo.contrib.mindtpy.tests.feasibility_pump1 import FeasPump1
 from pyomo.contrib.mindtpy.tests.feasibility_pump2 import FeasPump2
 
-required_solvers = ('ipopt', 'cplex')
+required_solvers = ('ipopt', 'glpk')
 # TODO: 'appsi_highs' will fail here.
 if all(SolverFactory(s).available(exception_flag=False) for s in required_solvers):
     subsolvers_available = True
@@ -69,6 +69,22 @@ def test_FP(self):
                 log_infeasible_constraints(model)
                 self.assertTrue(is_feasible(model, self.get_config(opt)))
 
+    def test_FP_L1_norm(self):
+        """Test the feasibility pump algorithm."""
+        with SolverFactory('mindtpy') as opt:
+            for model in model_list:
+                model = model.clone()
+                results = opt.solve(
+                    model,
+                    strategy='FP',
+                    mip_solver=required_solvers[1],
+                    nlp_solver=required_solvers[0],
+                    absolute_bound_tolerance=1e-5,
+                    fp_main_norm='L1',
+                )
+                log_infeasible_constraints(model)
+                self.assertTrue(is_feasible(model, self.get_config(opt)))
+
     def test_FP_OA_8PP(self):
         """Test the FP-OA algorithm."""
         with SolverFactory('mindtpy') as opt: