diff --git a/CHANGELOG.md b/CHANGELOG.md
index 25737c095f..ff77cb3035 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,7 @@ Changes
 
 - fix RuntimeError in export_phrases (change defaultdict to dict) (PR [#3041](https://github.com/RaRe-Technologies/gensim/pull/3041), [@thalishsajeed](https://github.com/thalishsajeed))
 - Record lifecycle events in Gensim models (PR [#3060](https://github.com/RaRe-Technologies/gensim/pull/3060), [@piskvorky](https://github.com/piskvorky))
+- Default to pickle protocol 4 when saving models (PR [#3065](https://github.com/RaRe-Technologies/gensim/pull/3065), [@piskvorky](https://github.com/piskvorky))
 
 ## 4.0.0beta, 2020-10-31
 
diff --git a/gensim/similarities/annoy.py b/gensim/similarities/annoy.py
index b237c11a99..e586b2d2e3 100644
--- a/gensim/similarities/annoy.py
+++ b/gensim/similarities/annoy.py
@@ -84,7 +84,7 @@ def __init__(self, model=None, num_trees=None):
                 raise ValueError("Only a Word2Vec, Doc2Vec, FastText or KeyedVectors instance can be used")
             self._build_from_model(kv.get_normed_vectors(), kv.index_to_key, kv.vector_size)
 
-    def save(self, fname, protocol=2):
+    def save(self, fname, protocol=utils.PICKLE_PROTOCOL):
         """Save AnnoyIndexer instance to disk.
 
         Parameters
diff --git a/gensim/similarities/nmslib.py b/gensim/similarities/nmslib.py
index 620f32e519..752976862b 100644
--- a/gensim/similarities/nmslib.py
+++ b/gensim/similarities/nmslib.py
@@ -85,6 +85,7 @@
 except ImportError:
     raise ImportError("NMSLIB not installed. To use the NMSLIB indexer, please run `pip install nmslib`.")
 
+from gensim import utils
 from gensim.models.doc2vec import Doc2Vec
 from gensim.models.word2vec import Word2Vec
 from gensim.models.fasttext import FastText
@@ -141,7 +142,7 @@ def __init__(self, model, index_params=None, query_time_params=None):
             else:
                 raise ValueError("model must be a Word2Vec, Doc2Vec, FastText or KeyedVectors instance")
 
-    def save(self, fname, protocol=2):
+    def save(self, fname, protocol=utils.PICKLE_PROTOCOL):
         """Save this NmslibIndexer instance to a file.
 
         Parameters
diff --git a/gensim/utils.py b/gensim/utils.py
index cf5d6b6499..910dab4dff 100644
--- a/gensim/utils.py
+++ b/gensim/utils.py
@@ -39,6 +39,12 @@
 
 logger = logging.getLogger(__name__)
 
+# When pickling objects for persistence, use this protocol by default.
+# Note that users won't be able to load models saved with high protocols on older environments that do
+# not support that protocol (e.g. Python 2).
+# In the rare cases where this matters, users can explicitly pass `model.save(pickle_protocol=2)`.
+# See also https://github.com/RaRe-Technologies/gensim/pull/3065
+PICKLE_PROTOCOL = 4
 
 PAT_ALPHABETIC = re.compile(r'(((?![\d])\w)+)', re.UNICODE)
 RE_HTML_ENTITY = re.compile(r'&(#?)([xX]?)(\w{1,8});', re.UNICODE)
@@ -567,7 +573,10 @@ def _adapt_by_suffix(fname):
         compress, suffix = (True, 'npz') if fname.endswith('.gz') or fname.endswith('.bz2') else (False, 'npy')
         return compress, lambda *args: '.'.join(args + (suffix,))
 
-    def _smart_save(self, fname, separately=None, sep_limit=10 * 1024**2, ignore=frozenset(), pickle_protocol=2):
+    def _smart_save(
+            self, fname,
+            separately=None, sep_limit=10 * 1024**2, ignore=frozenset(), pickle_protocol=PICKLE_PROTOCOL,
+        ):
         """Save the object to a file. Used internally by :meth:`gensim.utils.SaveLoad.save()`.
 
         Parameters
@@ -595,8 +604,9 @@ def _smart_save(self, fname, separately=None, sep_limit=10 * 1024**2, ignore=fro
         """
         compress, subname = SaveLoad._adapt_by_suffix(fname)
 
-        restores = self._save_specials(fname, separately, sep_limit, ignore, pickle_protocol,
-                                       compress, subname)
+        restores = self._save_specials(
+            fname, separately, sep_limit, ignore, pickle_protocol, compress, subname,
+        )
         try:
             pickle(self, fname, protocol=pickle_protocol)
         finally:
@@ -711,7 +721,10 @@ def _save_specials(self, fname, separately, sep_limit, ignore, pickle_protocol,
             raise
         return restores + [(self, asides)]
 
-    def save(self, fname_or_handle, separately=None, sep_limit=10 * 1024**2, ignore=frozenset(), pickle_protocol=2):
+    def save(
+            self, fname_or_handle,
+            separately=None, sep_limit=10 * 1024**2, ignore=frozenset(), pickle_protocol=PICKLE_PROTOCOL,
+        ):
         """Save the object to a file.
 
         Parameters
@@ -1410,7 +1423,7 @@ def smart_extension(fname, ext):
     return fname
 
 
-def pickle(obj, fname, protocol=2):
+def pickle(obj, fname, protocol=PICKLE_PROTOCOL):
     """Pickle object `obj` to file `fname`, using smart_open so that `fname` can be on S3, HDFS, compressed etc.
 
     Parameters
@@ -1420,7 +1433,7 @@ def pickle(obj, fname, protocol=2):
     fname : str
         Path to pickle file.
     protocol : int, optional
-        Pickle protocol number. Default is 2 in order to support compatibility across python 2.x and 3.x.
+        Pickle protocol number.
 
     """
     with open(fname, 'wb') as fout:  # 'b' for binary, needed on Windows