diff --git a/solvers/newt_alm.py b/solvers/newt_alm.py
index e8103b8..3dafd3b 100644
--- a/solvers/newt_alm.py
+++ b/solvers/newt_alm.py
@@ -16,6 +16,9 @@ def njit(f):  # noqa: F811
         return f
 
 
+MAX_STANDARD_SAMPLES = 10_000
+
+
 class Solver(BaseSolver):
     name = "Newt-ALM"
     sampling_strategy = "callback"
@@ -34,6 +37,16 @@ def set_objective(self, X, y, alphas, fit_intercept):
         self.X, self.y, self.lambdas = X, y, alphas
         self.fit_intercept = fit_intercept
 
+    def skip(self, X, y, alphas, fit_intercept):
+        n_samples = X.shape[0]
+        if self.inner_solver == "standard" and n_samples > MAX_STANDARD_SAMPLES:
+            return True, (
+                f"{self.name}'s standard inner solver would form a dense "
+                f"{n_samples}-by-{n_samples} system"
+            )
+
+        return False, None
+
     def warm_up(self):
         self.run_once()
 
@@ -215,7 +228,7 @@ def _compute_direction(self, x, sigma, A, b, y, ATy, lambdas):
         inner_solver = copy.deepcopy(self.inner_solver)
 
         if inner_solver == "auto":
-            if m > 10000:  # Very large m - avoid forming mxm matrices
+            if m > MAX_STANDARD_SAMPLES:
                 inner_solver = "cg"
             elif m >= 3 * n and n < 5000:
                 inner_solver = "woodbury"
diff --git a/tests/test_newt_alm.py b/tests/test_newt_alm.py
new file mode 100644
index 0000000..683ebf2
--- /dev/null
+++ b/tests/test_newt_alm.py
@@ -0,0 +1,32 @@
+from types import SimpleNamespace
+
+import pytest
+
+from solvers.newt_alm import Solver
+
+
+@pytest.mark.parametrize(
+    ("inner_solver", "n_samples", "expected_skip"),
+    [
+        ("standard", 10_001, True),
+        ("standard", 10_000, False),
+        ("auto", 20_000, False),
+    ],
+)
+def test_skip_standard_solver_for_large_dense_systems(
+    inner_solver,
+    n_samples,
+    expected_skip,
+):
+    solver = Solver.get_instance(inner_solver=inner_solver)
+    X = SimpleNamespace(shape=(n_samples, 100))
+
+    skip, reason = solver.skip(
+        X=X,
+        y=None,
+        alphas=None,
+        fit_intercept=False,
+    )
+
+    assert skip is expected_skip
+    assert (reason is not None) is expected_skip