diff --git a/satpy/tests/writer_tests/test_awips_tiled.py b/satpy/tests/writer_tests/test_awips_tiled.py
index 63113a9f94..dbc1bc82d7 100644
--- a/satpy/tests/writer_tests/test_awips_tiled.py
+++ b/satpy/tests/writer_tests/test_awips_tiled.py
@@ -198,7 +198,7 @@ def test_basic_numbered_1_tile(self, extra_attrs, expected_filename, use_save_da
             check_required_properties(unmasked_ds, output_ds)
             scale_factor = output_ds["data"].encoding["scale_factor"]
             np.testing.assert_allclose(input_data_arr.values, output_ds["data"].data,
-                                       atol=scale_factor / 2)
+                                       atol=scale_factor * 0.75)
 
     def test_units_length_warning(self, tmp_path):
         """Test long 'units' warnings are raised."""
diff --git a/satpy/writers/awips_tiled.py b/satpy/writers/awips_tiled.py
index 15680e8091..03ce3e9d68 100644
--- a/satpy/writers/awips_tiled.py
+++ b/satpy/writers/awips_tiled.py
@@ -630,7 +630,13 @@ def _get_factor_offset_fill(input_data_arr, vmin, vmax, encoding):
         # max value
         fills = [2 ** (file_bit_depth - 1) - 1]
 
-    mx = (vmax - vmin) / (2 ** bit_depth - 1 - num_fills)
+    # NOTE: AWIPS is buggy and does not properly handle both
+    #   halves an integers data space. The below code limits
+    #   unsigned integers to the positive half and this seems
+    #   to work better with current AWIPS.
+    mx = (vmax - vmin) / (2 ** (bit_depth - 1) - 1 - num_fills)
+    # NOTE: This is what the line should look like if AWIPS wasn't buggy:
+    # mx = (vmax - vmin) / (2 ** bit_depth - 1 - num_fills)
     bx = vmin
     if not is_unsigned and not unsigned_in_signed:
         bx += 2 ** (bit_depth - 1) * mx