diff --git a/tests/matlab/rm3_pto_extension_step_audit.m b/tests/matlab/rm3_pto_extension_step_audit.m
index 6d2c681c..e64846e4 100644
--- a/tests/matlab/rm3_pto_extension_step_audit.m
+++ b/tests/matlab/rm3_pto_extension_step_audit.m
@@ -11,7 +11,7 @@ function rm3_pto_extension_step_audit()
 metrics.channels = {'floatHeaveM', 'floatHeaveSpeedMPerS', ...
     'sparHeaveM', 'sparHeaveSpeedMPerS', 'ptoStrokeM', ...
     'ptoStrokeSpeedMPerS', 'ptoForceN', 'ptoPowerW'};
-metrics.stepsS = [0.1, 0.05, 0.025];
+metrics.stepsS = [0.1, 0.05, 0.025, 0.0125];
 
 for caseName = ["float", "spar"]
     label = char(caseName);
@@ -28,12 +28,13 @@ function rm3_pto_extension_step_audit()
         'The published PTO-extension baseline is incomplete');
     writematrix(coarse, fullfile(outDir, label + "_dt_0p1.csv"));
     previous = coarse;
-    levelNames = ["coarseToMid", "midToFine"];
-    steps = [0.05, 0.025];
+    levelNames = ["coarseToMid", "midToFine", "fineToFiner"];
+    steps = [0.05, 0.025, 0.0125];
+    suffixes = ["0p05", "0p025", "0p0125"];
     for level = 1:numel(steps)
         dt = steps(level);
         write_input(inputFile, strrep(original, 'simu.dt = 0.1;', ...
-            sprintf('simu.dt = %.3f;', dt)));
+            sprintf('simu.dt = %.4f;', dt)));
         cd(caseDir);
         wecSim;
         assert(strcmp(simu.solver, 'ode4') && simu.dt == dt && ...
@@ -45,13 +46,8 @@ function rm3_pto_extension_step_audit()
         assert(isequal(size(current), [round(30 / dt) + 1, 9]) && ...
             max(abs(current(1:2:end, 1) - previous(:, 1))) < 1e-10, ...
             'The refined PTO-extension output is incomplete');
-        if dt == 0.05
-            suffix = '0p05';
-        else
-            suffix = '0p025';
-        end
         writematrix(current, fullfile(outDir, ...
-            label + "_dt_" + suffix + ".csv"));
+            label + "_dt_" + suffixes(level) + ".csv"));
         delta = current(1:2:end, 2:9) - previous(:, 2:9);
         metrics.(label).(char(levelNames(level))) = max(abs(delta), [], 1);
         previous = current;
diff --git a/tests/test_rm3_pto_extension_step_parity.py b/tests/test_rm3_pto_extension_step_parity.py
index 63ad4c79..ac668185 100644
--- a/tests/test_rm3_pto_extension_step_parity.py
+++ b/tests/test_rm3_pto_extension_step_parity.py
@@ -1,4 +1,4 @@
-"""Pair RM3 PTO-extension free decay at three pinned MATLAB solver steps."""
+"""Pair RM3 PTO-extension free decay as the source step is refined."""
 
 import os
 from pathlib import Path
@@ -36,12 +36,14 @@ def _python_response(hydro, coordinate, dt):
     })
 
 
-@pytest.mark.parametrize("name,coordinate,active,position_gate,speed_gate", [
-    ("float", {"float_heave": 5}, 0, .016, .030),
-    ("spar", {"spar_heave": -5}, 1, .0025, .0007),
+@pytest.mark.parametrize("name,coordinate,active,position_gate,speed_gate,"
+                         "finer_position_gate,finer_speed_gate", [
+    ("float", {"float_heave": 5}, 0, .016, .030, .009, .017),
+    ("spar", {"spar_heave": -5}, 1, .0025, .0007, .0015, .0004),
 ])
 def test_published_pto_extension_fine_step_pair(
     name, coordinate, active, position_gate, speed_gate,
+    finer_position_gate, finer_speed_gate,
 ):
     hydro = (Path(APPLICATIONS)
              / "_Common_Input_Files/RM3/hydroData/rm3.h5")
@@ -50,7 +52,8 @@ def test_published_pto_extension_fine_step_pair(
                       - np.asarray(h5["body2/properties/cg"]).ravel()[2])
     source = {}
     python = {}
-    for dt, suffix in ((.1, "0p1"), (.05, "0p05"), (.025, "0p025")):
+    for dt, suffix in ((.1, "0p1"), (.05, "0p05"), (.025, "0p025"),
+                       (.0125, "0p0125")):
         source[dt] = np.loadtxt(
             Path(SOURCE) / f"{name}_dt_{suffix}.csv", delimiter=",",
         )
@@ -66,13 +69,17 @@ def test_published_pto_extension_fine_step_pair(
     source_fine_change = np.max(np.abs(
         source[.05][:, 1:7] - source[.025][::2, 1:7]), axis=0,
     )
+    source_finer_change = np.max(np.abs(
+        source[.025][:, 1:7] - source[.0125][::2, 1:7]), axis=0,
+    )
     active_columns = (1, 2, 5, 6) if active == 0 else (3, 4, 5, 6)
     for column in active_columns:
         assert source_fine_change[column - 1] < source_coarse_change[column - 1]
+        assert source_finer_change[column - 1] < .75 * source_fine_change[column - 1]
 
     position_errors = {}
     speed_errors = {}
-    for dt in (.05, .025):
+    for dt in (.05, .025, .0125):
         response = python[dt]
         expected = source[dt]
         position_errors[dt] = np.max(np.abs(
@@ -101,6 +108,9 @@ def test_published_pto_extension_fine_step_pair(
         if dt == .025:
             assert np.max(np.abs(stroke - expected[:, 5])) < position_gate
             assert np.max(np.abs(stroke_speed - expected[:, 6])) < speed_gate
+        elif dt == .0125:
+            assert np.max(np.abs(stroke - expected[:, 5])) < finer_position_gate
+            assert np.max(np.abs(stroke_speed - expected[:, 6])) < finer_speed_gate
         assert np.max(np.abs(response.pto_force - expected[:, 7])) < 1e-7
         assert np.max(np.abs(response.pto_force * stroke_speed
                              - expected[:, 8])) < 1e-7
@@ -109,3 +119,7 @@ def test_published_pto_extension_fine_step_pair(
     assert speed_errors[.025] < speed_gate
     assert position_errors[.025] < .75 * position_errors[.05]
     assert speed_errors[.025] < .75 * speed_errors[.05]
+    assert position_errors[.0125] < finer_position_gate
+    assert speed_errors[.0125] < finer_speed_gate
+    assert position_errors[.0125] < .75 * position_errors[.025]
+    assert speed_errors[.0125] < .75 * speed_errors[.025]