diff --git a/CHANGES.md b/CHANGES.md
index eee5e7f..2dacf1d 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -3,6 +3,9 @@
 
 - Add ability to compare to Pandas DataFrames and store them as HDF5 files [#23]
 
+- Fix ``array_compare`` so that the ``atol`` parameter is correctly used with
+  FITS files. [#33]
+
 0.5 (2022-01-12)
 ----------------
 
diff --git a/README.rst b/README.rst
index 39dd16b..48136ea 100644
--- a/README.rst
+++ b/README.rst
@@ -111,12 +111,12 @@ The supported formats at this time are ``text`` and ``fits``, and
 contributions for other formats are welcome. The default format is
 ``text``.
 
-Another argument is the relative tolerance for floating point values
-(which defaults to 1e-7):
+Additional arguments are the relative and absolute tolerances for floating
+point values (which default to 1e-7 and 0, respectively):
 
 .. code:: python
 
-    @pytest.mark.array_compare(rtol=20)
+    @pytest.mark.array_compare(rtol=20, atol=0.1)
     def test_array():
         ...
 
diff --git a/pytest_arraydiff/plugin.py b/pytest_arraydiff/plugin.py
index c80d008..da78dfb 100755
--- a/pytest_arraydiff/plugin.py
+++ b/pytest_arraydiff/plugin.py
@@ -116,8 +116,9 @@ def compare(cls, reference_file, test_file, atol=None, rtol=None):
         from astropy.io.fits.diff import FITSDiff
         from astropy.utils.introspection import minversion
         if minversion(astropy, '2.0'):
-            diff = FITSDiff(reference_file, test_file, rtol=rtol)
+            diff = FITSDiff(reference_file, test_file, rtol=rtol, atol=atol)
         else:
+            # `atol` is not supported prior to Astropy 2.0
             diff = FITSDiff(reference_file, test_file, tolerance=rtol)
         return diff.identical, diff.report()
 
diff --git a/tests/baseline/test_tolerance.fits b/tests/baseline/test_absolute_tolerance.fits
similarity index 100%
rename from tests/baseline/test_tolerance.fits
rename to tests/baseline/test_absolute_tolerance.fits
diff --git a/tests/baseline/test_relative_tolerance.fits b/tests/baseline/test_relative_tolerance.fits
new file mode 100644
index 0000000..9fab1ae
Binary files /dev/null and b/tests/baseline/test_relative_tolerance.fits differ
diff --git a/tests/test_pytest_arraydiff.py b/tests/test_pytest_arraydiff.py
index 12f133f..e974706 100644
--- a/tests/test_pytest_arraydiff.py
+++ b/tests/test_pytest_arraydiff.py
@@ -132,9 +132,20 @@ def test_default_format(file_format):
     assert os.path.exists(os.path.join(gen_dir, 'test_default.' + ('fits' if file_format == 'fits' else 'txt')))
 
 
-@pytest.mark.array_compare(reference_dir=reference_dir, rtol=0.5, file_format='fits')
-def test_tolerance():
-    return np.ones((3, 4)) * 1.6
+@pytest.mark.array_compare(reference_dir=reference_dir, rtol=0.5,
+        file_format='fits')
+def test_relative_tolerance():
+    # Scale up the output values by 1.5 to ensure the large `rtol` value is
+    # needed. (The comparison file contains all 1.6.)
+    return np.ones((3, 4)) * 1.6 * 1.5
+
+
+@pytest.mark.array_compare(reference_dir=reference_dir, atol=1.5,
+        file_format='fits')
+def test_absolute_tolerance():
+    # Increase the output values by 1.4 to ensure the large `atol` value is
+    # needed. (The comparison file contains all 1.6.)
+    return np.ones((3, 4)) * 1.6 + 1.4
 
 
 def test_nofile():