diff --git a/neurodsp/tests/aperiodic/test_autocorr.py b/neurodsp/tests/aperiodic/test_autocorr.py
index 3137e1ba..5db31cca 100644
--- a/neurodsp/tests/aperiodic/test_autocorr.py
+++ b/neurodsp/tests/aperiodic/test_autocorr.py
@@ -20,6 +20,7 @@ def test_compute_decay_time(tsig):
     assert isinstance(decay_time, float)
 
 def test_fit_autocorr(tsig):
+    # This is a smoke test - check it runs with no accuracy checking
 
     timepoints, autocorrs = compute_autocorr(tsig, max_lag=500)
 
@@ -36,3 +37,21 @@ def test_fit_autocorr(tsig):
     popts2 = fit_autocorr(timepoints, autocorrs, fit_function='double_exp')
     fit_vals2 = compute_ac_fit(timepoints, *popts2, fit_function='double_exp')
     assert np.all(fit_vals2)
+
+def test_fit_autocorr_acc():
+    # This test includes some basic accuracy checking
+
+    fs = 100
+    tau = 0.015
+    lags = np.linspace(0, 100, 1000)
+
+    # Test can fit and recompute the tau value
+    corrs1 = exp_decay_func(lags, tau, 1, 0)
+    params1 = fit_autocorr(lags, corrs1)
+    assert np.isclose(params1[0], tau, 0.001)
+
+    # Test can fit and recompute the tau value - timepoints as time values
+    lags = lags / fs
+    corrs2 = exp_decay_func(lags, tau, 1, 0)
+    params2 = fit_autocorr(lags, corrs2)
+    assert np.isclose(params2[0], tau, 0.001)