diff --git a/ilpy/impl/solvers/GurobiBackend.cpp b/ilpy/impl/solvers/GurobiBackend.cpp
index 9faf868..e8f63c8 100644
--- a/ilpy/impl/solvers/GurobiBackend.cpp
+++ b/ilpy/impl/solvers/GurobiBackend.cpp
@@ -218,21 +218,31 @@ GurobiBackend::solve(Solution& x, std::string& msg) {
 
 	GRB_CHECK(GRBupdatemodel(_model));
 
+	GRBenv* modelenv = GRBgetenv(_model);
+
 	if (_timeout > 0) {
 
-		GRBenv* modelenv = GRBgetenv(_model);
 		GRB_CHECK(GRBsetdblparam(modelenv, GRB_DBL_PAR_TIMELIMIT, _timeout));
 	}
 
 	if (_gap >= 0) {
 
-		GRBenv* modelenv = GRBgetenv(_model);
 		if (_absoluteGap)
 			GRB_CHECK(GRBsetdblparam(modelenv, GRB_DBL_PAR_MIPGAPABS, _gap));
 		else
 			GRB_CHECK(GRBsetdblparam(modelenv, GRB_DBL_PAR_MIPGAP, _gap));
 	}
 
+	// Sets the strategy for handling non-convex quadratic objectives
+	// or non-convex quadratic constraints. 
+	// 0 = an error is reported if the original user model contains non-convex
+	//     quadratic constructs.
+	// 1 = an error is reported if non-convex quadratic constructs could not be
+	//     discarded or linearized during presolve.
+	// 2 = non-convex quadratic problems are solved by means of translating them
+	//     into bilinear form and applying spatial branching.
+	GRB_CHECK(GRBsetintparam(modelenv, GRB_INT_PAR_NONCONVEX, 2));
+
 	GRB_CHECK(GRBoptimize(_model));
 
 	int status;
diff --git a/tests/test_solvers.py b/tests/test_solvers.py
index 40af4d8..47cb8a4 100644
--- a/tests/test_solvers.py
+++ b/tests/test_solvers.py
@@ -13,11 +13,11 @@
     HAVE_GUROBI = False
 
 
+PREFS = [ilpy.Preference.Scip, pytest.param(ilpy.Preference.Gurobi, marks=gu_marks)]
+
+
 @pytest.mark.parametrize("as_expression", [True, False], ids=["as_expr", "as_constr"])
-@pytest.mark.parametrize(
-    "preference",
-    [ilpy.Preference.Scip, pytest.param(ilpy.Preference.Gurobi, marks=gu_marks)],
-)
+@pytest.mark.parametrize("preference", PREFS)
 def test_simple_solver(preference: ilpy.Preference, as_expression: bool) -> None:
     num_vars = 10
     special_var = 5
@@ -62,10 +62,7 @@ def test_simple_solver(preference: ilpy.Preference, as_expression: bool) -> None
 
 
 @pytest.mark.parametrize("as_expression", [True, False], ids=["as_expr", "as_constr"])
-@pytest.mark.parametrize(
-    "preference",
-    [ilpy.Preference.Scip, pytest.param(ilpy.Preference.Gurobi, marks=gu_marks)],
-)
+@pytest.mark.parametrize("preference", PREFS)
 def test_quadratic_solver(preference: ilpy.Preference, as_expression: bool) -> None:
     num_vars = 10
     special_var = 5
@@ -105,15 +102,13 @@ def test_quadratic_solver(preference: ilpy.Preference, as_expression: bool) -> N
     assert solution[5] == -2  # jan please check
 
 
-@pytest.mark.skipif(not HAVE_GUROBI, reason="Gurobi not installed")
-def test_non_convex_quadratic_gurobi() -> None:
+@pytest.mark.parametrize("preference", PREFS)
+def test_non_convex_quadratic(preference: ilpy.Preference) -> None:
     # currently, just a smoke test to make sure we don't crash on solve.
     obj = ilpy.Objective()
     obj.set_quadratic_coefficient(0, 0, -1)  # quadratic term (-x^2)
 
-    solver = ilpy.Solver(
-        1, ilpy.VariableType.Continuous, preference=ilpy.Preference.Gurobi
-    )
+    solver = ilpy.Solver(1, ilpy.VariableType.Continuous, preference=preference)
     solver.set_objective(obj)
 
     constraint = ilpy.Constraint()
@@ -121,6 +116,5 @@ def test_non_convex_quadratic_gurobi() -> None:
     constraint.set_value(1)
     solver.add_constraint(constraint)
 
-    # Gurobi will raise an exception at the moment... may be changed later:
-    with pytest.raises(RuntimeError, match="Q matrix is not positive semi-definite"):
-        solver.solve()
+    # Gurobi will give zeros and SCIP will give something like -9999999987
+    assert solver.solve() is not None