diff --git a/spacy/tests/lang/en/test_exceptions.py b/spacy/tests/lang/en/test_exceptions.py
index 1b56a3b0f..6229b96eb 100644
--- a/spacy/tests/lang/en/test_exceptions.py
+++ b/spacy/tests/lang/en/test_exceptions.py
@@ -113,9 +113,8 @@ def test_en_tokenizer_norm_exceptions(en_tokenizer, text, norms):
     assert [token.norm_ for token in tokens] == norms
 
 
-@pytest.mark.skip
 @pytest.mark.parametrize(
-    "text,norm", [("radicalised", "radicalized"), ("cuz", "because")]
+    "text,norm", [("Jan.", "January"), ("'cuz", "because")]
 )
 def test_en_lex_attrs_norm_exceptions(en_tokenizer, text, norm):
     tokens = en_tokenizer(text)
diff --git a/spacy/tests/lang/uk/test_tokenizer.py b/spacy/tests/lang/uk/test_tokenizer.py
index 91ae057f8..3d6e87301 100644
--- a/spacy/tests/lang/uk/test_tokenizer.py
+++ b/spacy/tests/lang/uk/test_tokenizer.py
@@ -89,7 +89,6 @@ def test_uk_tokenizer_splits_open_appostrophe(uk_tokenizer, text):
     assert tokens[0].text == "'"
 
 
-@pytest.mark.skip(reason="See Issue #3327 and PR #3329")
 @pytest.mark.parametrize("text", ["Тест''"])
 def test_uk_tokenizer_splits_double_end_quote(uk_tokenizer, text):
     tokens = uk_tokenizer(text)
diff --git a/spacy/tests/serialize/test_serialize_pipeline.py b/spacy/tests/serialize/test_serialize_pipeline.py
index 2deaa180d..a26dceed0 100644
--- a/spacy/tests/serialize/test_serialize_pipeline.py
+++ b/spacy/tests/serialize/test_serialize_pipeline.py
@@ -140,9 +140,6 @@ def test_to_from_bytes(parser, blank_parser):
     assert blank_parser.moves.n_moves == parser.moves.n_moves
 
 
-@pytest.mark.skip(
-    reason="This seems to be a dict ordering bug somewhere. Only failing on some platforms."
-)
 def test_serialize_tagger_roundtrip_bytes(en_vocab, taggers):
     tagger1 = taggers[0]
     tagger1_b = tagger1.to_bytes()
diff --git a/spacy/tests/serialize/test_serialize_tokenizer.py b/spacy/tests/serialize/test_serialize_tokenizer.py
index 00a88ec38..035561606 100644
--- a/spacy/tests/serialize/test_serialize_tokenizer.py
+++ b/spacy/tests/serialize/test_serialize_tokenizer.py
@@ -26,7 +26,6 @@ def test_serialize_custom_tokenizer(en_vocab, en_tokenizer):
     assert tokenizer_reloaded.rules == {}
 
 
-@pytest.mark.skip(reason="Currently unreliable across platforms")
 @pytest.mark.parametrize("text", ["I💜you", "they’re", "“hello”"])
 def test_serialize_tokenizer_roundtrip_bytes(en_tokenizer, text):
     tokenizer = en_tokenizer
@@ -38,7 +37,6 @@ def test_serialize_tokenizer_roundtrip_bytes(en_tokenizer, text):
     assert [token.text for token in doc1] == [token.text for token in doc2]
 
 
-@pytest.mark.skip(reason="Currently unreliable across platforms")
 def test_serialize_tokenizer_roundtrip_disk(en_tokenizer):
     tokenizer = en_tokenizer
     with make_tempdir() as d:
diff --git a/spacy/tests/vocab_vectors/test_lookups.py b/spacy/tests/vocab_vectors/test_lookups.py
index d8c7651e4..94e31a072 100644
--- a/spacy/tests/vocab_vectors/test_lookups.py
+++ b/spacy/tests/vocab_vectors/test_lookups.py
@@ -71,7 +71,6 @@ def test_table_api_to_from_bytes():
     assert "def" not in new_table2
 
 
-@pytest.mark.skip(reason="This fails on Python 3.5")
 def test_lookups_to_from_bytes():
     lookups = Lookups()
     lookups.add_table("table1", {"foo": "bar", "hello": "world"})
@@ -91,7 +90,6 @@ def test_lookups_to_from_bytes():
     assert new_lookups.to_bytes() == lookups_bytes
 
 
-@pytest.mark.skip(reason="This fails on Python 3.5")
 def test_lookups_to_from_disk():
     lookups = Lookups()
     lookups.add_table("table1", {"foo": "bar", "hello": "world"})
@@ -111,7 +109,6 @@ def test_lookups_to_from_disk():
     assert table2["b"] == 2
 
 
-@pytest.mark.skip(reason="This fails on Python 3.5")
 def test_lookups_to_from_bytes_via_vocab():
     table_name = "test"
     vocab = Vocab()
@@ -128,7 +125,6 @@ def test_lookups_to_from_bytes_via_vocab():
     assert new_vocab.to_bytes() == vocab_bytes
 
 
-@pytest.mark.skip(reason="This fails on Python 3.5")
 def test_lookups_to_from_disk_via_vocab():
     table_name = "test"
     vocab = Vocab()