diff --git a/CHANGES.rst b/CHANGES.rst
index cf15011996..dbbb1a5d5b 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -46,6 +46,11 @@ badpix_selfcal
 - Subtract pedestal dark when constructing min array across selfcal exposures
   for MIRI MRS data. [#8771]
 
+calwebb_coron3
+--------------
+
+- Tighten tolerance of psf alignment. [#8717]
+
 calwebb_detector1
 -----------------
 
diff --git a/jwst/coron/imageregistration.py b/jwst/coron/imageregistration.py
index 12fc185272..457b7664eb 100644
--- a/jwst/coron/imageregistration.py
+++ b/jwst/coron/imageregistration.py
@@ -40,7 +40,9 @@ def align_fourierLSQ(reference, target, mask=None):
 
     init_pars = [0., 0., 1.]
     results, _ = optimize.leastsq(shift_subtract, init_pars,
-                                  args=(reference, target, mask))
+                                  args=(reference, target, mask),
+                                  xtol=1E-15, ftol=1E-15,
+                                  )
     return results
 
 
@@ -165,7 +167,7 @@ def align_array(reference, target, mask=None, return_aligned=True):
 
     elif len(target.shape) == 3:
         nslices = target.shape[0]
-        shifts = np.empty((nslices, 3), dtype=float)
+        shifts = np.empty((nslices, 3), dtype=np.float64)
         if return_aligned:
             aligned = np.empty_like(target)
 
@@ -221,19 +223,19 @@ def align_models(reference, target, mask):
     # Compute the shifts of the PSF ("target") images relative to
     # the science ("reference") image in the first integration
     shifts = align_array(
-        reference.data[0].astype(np.float64),
-        target.data.astype(np.float64),
+        reference.data[0],
+        target.data,
         mask=mask.data, return_aligned=False)
 
     # Apply the shifts to the PSF images
     output_model.data = fourier_imshift(
-        target.data.astype(np.float64),
+        target.data,
         -shifts)
 
     # Apply the same shifts to the PSF error arrays, if they exist
     if target.err is not None:
         output_model.err = fourier_imshift(
-            target.err.astype(np.float64),
+            target.err,
             -shifts)
 
     # TODO: in the future we need to add shifts and other info (such as
diff --git a/jwst/regtest/test_miri_coron3.py b/jwst/regtest/test_miri_coron3.py
index d10af9e65d..ff7e6224d6 100644
--- a/jwst/regtest/test_miri_coron3.py
+++ b/jwst/regtest/test_miri_coron3.py
@@ -30,7 +30,7 @@ def test_miri_coron3_sci_exp(run_pipeline, suffix, exposure, fitsdiff_default_kw
     rtdata.output = output
     rtdata.get_truth("truth/test_miri_coron3/" + output)
 
-    fitsdiff_default_kwargs["atol"] = 1e-5
+    fitsdiff_default_kwargs["atol"] = 1e-2
     diff = FITSDiff(rtdata.output, rtdata.truth, **fitsdiff_default_kwargs)
     assert diff.identical, diff.report()
 
@@ -45,6 +45,7 @@ def test_miri_coron3_product(run_pipeline, suffix, fitsdiff_default_kwargs):
     rtdata.output = output
     rtdata.get_truth("truth/test_miri_coron3/" + output)
 
-    fitsdiff_default_kwargs['atol'] = 1e-5
+    fitsdiff_default_kwargs['atol'] = 1e-4
+    fitsdiff_default_kwargs['rtol'] = 1e-4
     diff = FITSDiff(rtdata.output, rtdata.truth, **fitsdiff_default_kwargs)
     assert diff.identical, diff.report()
diff --git a/jwst/regtest/test_nircam_coron3.py b/jwst/regtest/test_nircam_coron3.py
index 9c4a77ba46..c69b11881c 100644
--- a/jwst/regtest/test_nircam_coron3.py
+++ b/jwst/regtest/test_nircam_coron3.py
@@ -32,7 +32,7 @@ def test_nircam_coron3_sci_exp(run_pipeline, suffix, obs, fitsdiff_default_kwarg
     rtdata.output = output
     rtdata.get_truth("truth/test_nircam_coron3/" + output)
 
-    fitsdiff_default_kwargs["atol"] = 1e-5
+    fitsdiff_default_kwargs["atol"] = 1e-2
     diff = FITSDiff(rtdata.output, rtdata.truth, **fitsdiff_default_kwargs)
     assert diff.identical, diff.report()
 
@@ -63,6 +63,7 @@ def test_nircam_coron3_product(run_pipeline, suffix, fitsdiff_default_kwargs):
     rtdata.output = output
     rtdata.get_truth("truth/test_nircam_coron3/" + output)
 
-    fitsdiff_default_kwargs['atol'] = 1e-5
+    fitsdiff_default_kwargs['atol'] = 1e-4
+    fitsdiff_default_kwargs['rtol'] = 1e-4
     diff = FITSDiff(rtdata.output, rtdata.truth, **fitsdiff_default_kwargs)
     assert diff.identical, diff.report()