diff --git a/.github/workflows/python-package.yml b/.github/workflows/python-package.yml
index 29a6931d1..66b09477a 100644
--- a/.github/workflows/python-package.yml
+++ b/.github/workflows/python-package.yml
@@ -10,7 +10,7 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: [3.6, 3.7, 3.8]
+        python-version: [3.6, 3.7, 3.8, 3.9]
 
     steps:
     - uses: actions/checkout@v2
diff --git a/annif/backend/tfidf.py b/annif/backend/tfidf.py
index c42f6aa97..995aede0c 100644
--- a/annif/backend/tfidf.py
+++ b/annif/backend/tfidf.py
@@ -3,14 +3,19 @@
 
 import os.path
 import tempfile
-import gensim.similarities
-from gensim.matutils import Sparse2Corpus
 import annif.util
 from annif.suggestion import VectorSuggestionResult
 from annif.exception import NotInitializedException, NotSupportedException
 from . import backend
 from . import mixins
 
+# Filter UserWarnings due to not-installed python-Levenshtein package
+import warnings
+with warnings.catch_warnings():
+    warnings.simplefilter('ignore')
+    import gensim.similarities
+    from gensim.matutils import Sparse2Corpus
+
 
 class SubjectBuffer:
     """A file-backed buffer to store and retrieve subject text."""
diff --git a/setup.py b/setup.py
index 3a02ee3f0..9a0de7fca 100644
--- a/setup.py
+++ b/setup.py
@@ -24,25 +24,25 @@ def read(fname):
         'swagger_ui_bundle',
         'flask',
         'flask-cors',
-        'click==7.1.*',
+        'click==8.0.*',
         'click-log',
-        'joblib==0.17.0',
+        'joblib==1.0.1',
         'nltk',
-        'gensim==3.8.*',
+        'gensim==4.0.*',
         'scikit-learn==0.24.2',
-        'scipy==1.5.3',
+        'scipy==1.5.4',
         'rdflib>=4.2,<6.0',
         'gunicorn',
-        'numpy==1.18.*',
-        'optuna==2.2.0',
+        'numpy==1.19.*',
+        'optuna==2.8.0',
         'stwfsapy==0.2.*'
     ],
     tests_require=['py', 'pytest', 'requests'],
     extras_require={
         'fasttext': ['fasttext==0.9.2'],
         'voikko': ['voikko'],
-        'vw': ['vowpalwabbit==8.8.1'],
-        'nn': ['tensorflow-cpu==2.3.1', 'lmdb==1.0.0'],
+        'vw': ['vowpalwabbit==8.10.2'],
+        'nn': ['tensorflow-cpu==2.5.0', 'lmdb==1.2.1'],
         'omikuji': ['omikuji==0.3.*'],
         'yake': ['yake==0.4.5'],
         'dev': [