diff --git a/setup.py b/setup.py
index dee1c0388..9c7d7fdcd 100644
--- a/setup.py
+++ b/setup.py
@@ -44,8 +44,8 @@
 install_requires = [
     # we are rather picky about msgpack versions, because a good working msgpack is
     # very important for borg, see https://github.com/borgbackup/borg/issues/3753
-    # as of now, 0.5.6 is the only preferred version of msgpack:
-    'msgpack==0.5.6',
+    # as of now, 0.5.6 and 0.6.0 are the only preferred versions of msgpack:
+    'msgpack >=0.5.6, !=0.5.7, !=0.5.8, !=0.5.9, <=0.6.0',
     # if you can't satisfy the above requirement, these are versions that might
     # also work ok, IF you make sure to use the COMPILED version of msgpack-python,
     # NOT the PURE PYTHON fallback implementation: ==0.5.1, ==0.5.4