diff --git a/requirements.txt b/requirements.txt
index 1f30aaf3b..ffb302037 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -3,7 +3,7 @@
 # process, which may cause wedges in the gate later.
 pbr!=2.1.0,>=2.0.0 # Apache-2.0
 
-eventlet!=0.18.3,>=0.18.2 # MIT
+eventlet!=0.18.3,<0.21.0,>=0.18.2 # MIT
 requests!=2.12.2,!=2.13.0,>=2.10.0 # Apache-2.0
 netaddr!=0.7.16,>=0.7.13 # BSD
 neutron-lib>=1.6.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index 5b96281fa..b5cb5a70f 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -3,12 +3,12 @@
 # process, which may cause wedges in the gate later.
 hacking!=0.13.0,<0.14,>=0.12.0 # Apache-2.0
 
-coverage>=4.0 # Apache-2.0
+coverage!=4.4,>=4.0 # Apache-2.0
 fixtures>=3.0.0 # Apache-2.0/BSD
 mock>=2.0 # BSD
 python-subunit>=0.0.18 # Apache-2.0/BSD
 requests-mock>=1.1 # Apache-2.0
-sphinx>=1.5.1 # BSD
+sphinx!=1.6.1,>=1.5.1 # BSD
 oslosphinx>=4.7.0 # Apache-2.0
 oslo.concurrency>=3.8.0 # Apache-2.0
 oslotest>=1.10.0 # Apache-2.0