diff --git a/lower-constraints.txt b/lower-constraints.txt
index 329e04176..6e32b761e 100644
--- a/lower-constraints.txt
+++ b/lower-constraints.txt
@@ -31,8 +31,6 @@ oslo.i18n==3.20.0
 oslo.log==3.36.0
 oslo.serialization==2.25.0
 oslo.utils==3.36.0
-oslotest==3.2.0
-paramiko==2.0.0
 pbr==2.0.0
 prettytable==0.7.2
 pyasn1==0.4.2
@@ -51,11 +49,9 @@ requests==2.18.4
 requestsexceptions==1.4.0
 restructuredtext-lint==1.1.3
 rfc3986==1.1.0
-setuptools==21.0.0
+setuptools==39.0.1
 stestr==2.0.0
 stevedore==1.28.0
-testrepository==0.0.18
-testscenarios==0.4
 testtools==2.2.0
 traceback2==1.4.0
 unittest2==1.1.0
diff --git a/requirements.txt b/requirements.txt
index 7531fba43..9186f7f13 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -4,6 +4,8 @@
 pbr!=2.1.0,>=2.0.0 # Apache-2.0
 oslo.config>=5.2.0 # Apache-2.0
 oslo.log>=3.36.0 # Apache-2.0
-paramiko>=2.0.0 # LGPLv2.1+
+PyYAML>=3.12 # MIT
+# TODO(dtantsur): remove pyOpenSSL when we no longer support Bionic and
+# openSUSE updates its version to at least 18.0.0.
 pyOpenSSL>=18.0.0 # Apache-2.0
-setuptools!=24.0.0,!=34.0.0,!=34.0.1,!=34.0.2,!=34.0.3,!=34.1.0,!=34.1.1,!=34.2.0,!=34.3.0,!=34.3.1,!=34.3.2,!=36.2.0,>=21.0.0 # PSF/ZPL
+setuptools!=48.0.0,!=49.0.0,>=39.0.1 # PSF/ZPL
diff --git a/test-requirements.txt b/test-requirements.txt
index 08571a142..d9fdd013a 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -6,12 +6,8 @@ hacking>=3.0,<4.0.0 # Apache-2.0
 
 coverage!=4.4,>=4.0 # Apache-2.0
 doc8>=0.6.0 # Apache-2.0
-oslotest>=3.2.0 # Apache-2.0
 stestr>=2.0.0 # Apache-2.0
-testrepository>=0.0.18 # Apache-2.0/BSD
-testscenarios>=0.4 # Apache-2.0/BSD
 testtools>=2.2.0 # MIT
-PyYAML>=3.12 # MIT
 Pygments>=2.2.0 # BSD license
 flake8-import-order>=0.17.1 # LGPLv3