diff --git a/.github/julia/runtests.jl b/.github/julia/runtests.jl
index c6a4080f..7a8e7427 100644
--- a/.github/julia/runtests.jl
+++ b/.github/julia/runtests.jl
@@ -35,22 +35,46 @@ Optimizer_LP() = Optimizer(["logger=SILENT", "preset=filterslp"])
     # This function tests (potentially) non-convex nonlinear programs. The tests
     # are meant to be "easy" in the sense that most NLP solvers can find the
     # same global minimum, but a test failure can sometimes be allowed.
-    exclude = [
-        # Remove once https://github.com/cvanaret/Uno/issues/39 is fixed
-        "005_010",
-        # Okay to exclude forever: AmplNLWriter does not support
-        # user-defined functions.
-        "006_010",
-        # Remove once https://github.com/cvanaret/Uno/issues/38 is fixed
-        "007_010",
-    ]
-    MINLPTests.test_nlp_expr(Optimizer; exclude, primal_target)
-    MINLPTests.test_nlp_expr(Optimizer_LP; exclude, primal_target)
+    MINLPTests.test_nlp_expr(
+        Optimizer;
+        exclude = [
+            # Remove once https://github.com/cvanaret/Uno/issues/39 is fixed
+            "005_010",
+            # Okay to exclude forever: AmplNLWriter does not support
+            # user-defined functions.
+            "006_010",
+            # Remove once https://github.com/cvanaret/Uno/issues/38 is fixed
+            "007_010",
+        ],
+        primal_target,
+    )
+    MINLPTests.test_nlp_expr(
+        Optimizer_LP;
+        exclude = [
+            "001_010",  # Local solution
+            "003_014",  # Local solution
+            # Remove once https://github.com/cvanaret/Uno/issues/39 is fixed
+            "005_010",
+            # Okay to exclude forever: AmplNLWriter does not support
+            # user-defined functions.
+            "006_010",
+            # Remove once https://github.com/cvanaret/Uno/issues/38 is fixed
+            "007_010",
+        ],
+        primal_target,
+        objective_tol = 1e-4,
+        primal_tol = 1e-4,
+    )
     # This function tests convex nonlinear programs. Test failures here should
     # never be allowed, because even local NLP solvers should find the global
     # optimum.
     MINLPTests.test_nlp_cvx_expr(Optimizer; primal_target)
-    MINLPTests.test_nlp_cvx_expr(Optimizer_LP; primal_target)
+    MINLPTests.test_nlp_cvx_expr(
+        Optimizer_LP; 
+        primal_target,
+        objective_tol = 1e-4,
+        primal_tol = 1e-4,
+    )
 end
 
 # This testset runs the full gamut of MOI.Test.runtests. There are a number of