diff --git a/CHANGES.rst b/CHANGES.rst
index 62bf7edc0..cecb65c53 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -4,6 +4,10 @@ Latest changes
 Development version
 -------------------
 
+- Fix argument 'max_nbytes' being used if explicitely set to something
+  else than None even though 'mmap_mode' was set to None.
+  https://github.com/joblib/joblib/pull/1325
+
 - Make sure that joblib works even when multiprocessing is not available,
   for instance with Pyodide
   https://github.com/joblib/joblib/pull/1256
diff --git a/joblib/parallel.py b/joblib/parallel.py
index 1c2fe18f7..0bb368064 100644
--- a/joblib/parallel.py
+++ b/joblib/parallel.py
@@ -495,9 +495,9 @@ class Parallel(Logger):
             parallel_backend.
         verbose: int, optional
             The verbosity level: if non zero, progress messages are
-            printed. Above 50, the output is sent to stdout.
+            printed. If above 50, the output is sent to stdout.
             The frequency of the messages increases with the verbosity level.
-            If it more than 10, all iterations are reported.
+            If above 10, all iterations are reported.
         timeout: float, optional
             Timeout limit for each task to complete.  If any task takes longer
             a TimeOutError will be raised. Only applied when n_jobs != 1
@@ -540,7 +540,8 @@ class Parallel(Logger):
             Threshold on the size of arrays passed to the workers that
             triggers automated memory mapping in temp_folder. Can be an int
             in Bytes, or a human-readable string, e.g., '1M' for 1 megabyte.
-            Use None to disable memmapping of large arrays.
+            Use None to disable automatic memmapping of large arrays (small
+            arrays can ignore this argument).
             Only active when backend="loky" or "multiprocessing".
         mmap_mode: {None, 'r+', 'r', 'w+', 'c'}, default: 'r'
             Memmapping mode for numpy arrays passed to workers. None will
@@ -688,6 +689,9 @@ def __init__(self, n_jobs=None, backend=None, verbose=0, timeout=None,
         self._id = uuid4().hex
         self._reducer_callback = None
 
+        if mmap_mode is None:
+            max_nbytes = None
+
         if isinstance(max_nbytes, str):
             max_nbytes = memstr_to_bytes(max_nbytes)
 
diff --git a/joblib/test/test_memmapping.py b/joblib/test/test_memmapping.py
index b752027d8..aded3dc8d 100644
--- a/joblib/test/test_memmapping.py
+++ b/joblib/test/test_memmapping.py
@@ -888,6 +888,35 @@ def test_memmapping_pool_for_large_arrays_disabled(factory, tmpdir):
         del p
 
 
+@with_numpy
+@with_multiprocessing
+@parametrize("factory", [MemmappingPool, TestExecutor.get_memmapping_executor],
+             ids=["multiprocessing", "loky"])
+def test_memmapping_pool_disabled_by_mmap_mode_to_None(factory, tmpdir):
+    """Check that memmapping is in effect disabled by setting
+    mmap_mode to None while setting max_nbytes to an explicit
+    value."""
+    # Set mmap_mode to None to disable memmapping feature
+    p = factory(3, mmap_mode=None, max_nbytes=40, temp_folder=tmpdir.strpath)
+    try:
+
+        # Check that the tempfolder is empty
+        assert os.listdir(tmpdir.strpath) == []
+
+        # Try with a file largish than the memmap threshold of 40 bytes
+        large = np.ones(100, dtype=np.float64)
+        assert large.nbytes == 800
+        p.map(check_array, [(large, i, 1.0) for i in range(large.shape[0])])
+
+        # Check that the tempfolder is still empty
+        assert os.listdir(tmpdir.strpath) == []
+
+    finally:
+        # Cleanup open file descriptors
+        p.terminate()
+        del p
+
+
 @with_numpy
 @with_multiprocessing
 @with_dev_shm