diff --git a/tests/test_interpolatedimage.py b/tests/test_interpolatedimage.py
index dd72937efa..b5e1a9704e 100644
--- a/tests/test_interpolatedimage.py
+++ b/tests/test_interpolatedimage.py
@@ -32,6 +32,9 @@
 KXVALS = np.array((1.30, 0.71, -4.30)) * np.pi / 2.
 KYVALS = np.array((0.80, -0.02, -0.31,)) * np.pi / 2.
 
+# The timing tests can be unreliable in environments with other processes running at the
+# same time.  So we disable them by default.  However, on a clean system, they should all pass.
+test_timing = False
 
 @pytest.fixture
 def ref():
@@ -1785,21 +1788,21 @@ def test_depixelize():
     # Second time with the same size image is much faster, since uses a cache.
     nopix_image2 = im1.depixelize(x_interpolant=interp)
     t8 = time.time()
-    if platform.python_implementation() != 'PyPy':
+    if test_timing and platform.python_implementation() != 'PyPy':
         # PyPy timings can be fairly arbitrary at times.
         assert t8-t7 < (t3-t2)/5
 
     # Even if the image is different.
     nopix_image3 = im4.depixelize(x_interpolant=interp)
     t9 = time.time()
-    if platform.python_implementation() != 'PyPy':
+    if test_timing and platform.python_implementation() != 'PyPy':
         assert t9-t8 < (t3-t2)/5
 
     # But not if you clear the cache.
     galsim.Image.clear_depixelize_cache()
     nopix_image4 = im4.depixelize(x_interpolant=interp)
     t10 = time.time()
-    if platform.python_implementation() != 'PyPy':
+    if test_timing and platform.python_implementation() != 'PyPy':
         assert t10-t9 > (t3-t2)/5
 
     print('times:')
diff --git a/tests/test_phase_psf.py b/tests/test_phase_psf.py
index 6d71bb34f4..78bac176ca 100644
--- a/tests/test_phase_psf.py
+++ b/tests/test_phase_psf.py
@@ -29,6 +29,10 @@
 
 theta0 = (0*galsim.arcmin, 0*galsim.arcmin)
 
+# The timing tests can be unreliable in environments with other processes running at the
+# same time.  So we disable them by default.  However, on a clean system, they should all pass.
+test_timing = False
+
 
 @timer
 def test_aperture():
@@ -1018,7 +1022,8 @@ def test_speedup():
     psf.drawImage(method='phot', n_photons=1e3)
     t1 = time.time()
     print("Time for geometric approximation draw: {:6.4f}s".format(t1-t0))
-    assert (t1-t0) < 0.1, "Photon-shooting took too long ({0} s).".format(t1-t0)
+    if test_timing:
+        assert (t1-t0) < 0.1, "Photon-shooting took too long ({0} s).".format(t1-t0)
 
 
 @timer
diff --git a/tests/test_sensor.py b/tests/test_sensor.py
index d8468fc65f..c0d63ccce2 100644
--- a/tests/test_sensor.py
+++ b/tests/test_sensor.py
@@ -25,6 +25,10 @@
 import galsim
 from galsim_test_helpers import *
 
+# The timing tests can be unreliable in environments with other processes running at the
+# same time.  So we disable them by default.  However, on a clean system, they should all pass.
+test_timing = False
+
 
 @timer
 def test_simple():
@@ -1010,7 +1014,8 @@ def test_resume(run_slow):
                                    decimal=5)
     print('Time with resume = ',t_resume)
     print('Time without resume = ',t_no_resume)
-    assert t_resume < t_no_resume
+    if test_timing:
+        assert t_resume < t_no_resume
 
     # The resume path should be exactly the same as doing all the photons at once.
     sensor3.accumulate(all_photons, im3)
diff --git a/tests/test_wcs.py b/tests/test_wcs.py
index 2c29e06d5d..ad894c638d 100644
--- a/tests/test_wcs.py
+++ b/tests/test_wcs.py
@@ -27,6 +27,10 @@
 import galsim
 from galsim_test_helpers import *
 
+# The timing tests can be unreliable in environments with other processes running at the
+# same time.  So we disable them by default.  However, on a clean system, they should all pass.
+test_timing = False
+
 
 # These positions will be used a few times below, so define them here.
 # One of the tests requires that the last pair are integers, so don't change that.
@@ -3199,10 +3203,10 @@ def test_int_args(run_slow):
     # Before fixing #1024, this took about 0.5 sec.
     # Now it usually takes about 0.04 sec.  Testing at 0.25 seems like a reasonable midpoint.
     print('Time = ',t1-t0)
-    if run_slow:
+    if test_timing:
         # Don't include this in regular unit tests, since it's not really something we need
         # to guarantee.  This timing estimate is appropriate for my laptop, but maybe not
-        # all systems.  It also fails for pypy on GHA for some reason.
+        # all systems.
         assert t1-t0 < 0.25
 
     posi = galsim.PositionI(5,6)