diff --git a/esmvalcore/preprocessor/__init__.py b/esmvalcore/preprocessor/__init__.py
index 39027da125..8cd0a8dda4 100644
--- a/esmvalcore/preprocessor/__init__.py
+++ b/esmvalcore/preprocessor/__init__.py
@@ -8,6 +8,8 @@
 
 from .._provenance import TrackedFile
 from .._task import BaseTask
+from ..cmor.check import cmor_check_data, cmor_check_metadata
+from ..cmor.fix import fix_data, fix_file, fix_metadata
 from ._area import (area_statistics, extract_named_regions, extract_region,
                     extract_shape, meridional_statistics, zonal_statistics)
 from ._cycles import amplitude
@@ -21,8 +23,6 @@
                     mask_landsea, mask_landseaice, mask_outside_range)
 from ._multimodel import multi_model_statistics
 from ._other import clip
-from ._reformat import (cmor_check_data, cmor_check_metadata, fix_data,
-                        fix_file, fix_metadata)
 from ._regrid import extract_levels, extract_point, regrid
 from ._time import (annual_statistics, anomalies, climate_statistics,
                     daily_statistics, decadal_statistics, extract_month,
@@ -54,6 +54,7 @@
     'extract_month',
     # Data reformatting/CMORization
     'fix_data',
+    'cmor_check_data',
     # Level extraction
     'extract_levels',
     # Weighting
@@ -106,7 +107,6 @@
     'anomalies',
     'regrid_time',
     'timeseries_filter',
-    'cmor_check_data',
     'convert_units',
     # Save to file
     'save',
@@ -130,8 +130,8 @@
 DEFAULT_ORDER = tuple(__all__)
 
 # The order of initial and final steps cannot be configured
-INITIAL_STEPS = DEFAULT_ORDER[:DEFAULT_ORDER.index('fix_data') + 1]
-FINAL_STEPS = DEFAULT_ORDER[DEFAULT_ORDER.index('cmor_check_data'):]
+INITIAL_STEPS = DEFAULT_ORDER[:DEFAULT_ORDER.index('cmor_check_data') + 1]
+FINAL_STEPS = DEFAULT_ORDER[DEFAULT_ORDER.index('save'):]
 
 MULTI_MODEL_FUNCTIONS = {
     'multi_model_statistics',
diff --git a/esmvalcore/preprocessor/_reformat.py b/esmvalcore/preprocessor/_reformat.py
deleted file mode 100644
index c6ab17337b..0000000000
--- a/esmvalcore/preprocessor/_reformat.py
+++ /dev/null
@@ -1,13 +0,0 @@
-"""Simple interface to reformat and CMORize functions."""
-from ..cmor.check import cmor_check, cmor_check_data, cmor_check_metadata
-from ..cmor.fix import fix_data, fix_file, fix_metadata
-
-
-__all__ = [
-    'cmor_check',
-    'cmor_check_metadata',
-    'cmor_check_data',
-    'fix_file',
-    'fix_metadata',
-    'fix_data',
-]
diff --git a/esmvalcore/preprocessor/_time.py b/esmvalcore/preprocessor/_time.py
index 888266c578..acf17caa0c 100644
--- a/esmvalcore/preprocessor/_time.py
+++ b/esmvalcore/preprocessor/_time.py
@@ -471,6 +471,7 @@ def anomalies(cube, period, reference=None, standardize=False):
             cube_stddev = climate_statistics(
                 cube, operator='std_dev', period=period)
             cube = cube / cube_stddev
+            cube.units = '1'
         return cube
 
     cube = _compute_anomalies(cube, reference, period)
@@ -490,6 +491,7 @@ def anomalies(cube, period, reference=None, standardize=False):
             )
         cube.data = cube.core_data() / da.concatenate(
             [cube_stddev.core_data() for _ in range(int(reps))], axis=tdim)
+        cube.units = '1'
     return cube
 
 
diff --git a/tests/unit/preprocessor/_time/test_time.py b/tests/unit/preprocessor/_time/test_time.py
index bffe806e9f..f6c4995492 100644
--- a/tests/unit/preprocessor/_time/test_time.py
+++ b/tests/unit/preprocessor/_time/test_time.py
@@ -1028,6 +1028,7 @@ def test_standardized_anomalies(period, standardize=True):
                 result.data,
                 expected
             )
+            assert result.units == '1'
         else:
             expected = np.ma.masked_invalid(expected_anomalies)
             assert_array_equal(