diff --git a/setup.py b/setup.py
index df5c61c..462c759 100644
--- a/setup.py
+++ b/setup.py
@@ -29,7 +29,7 @@
     # NOTE: Maintainers, please do not require google-api-core>=2.x.x
     # Until this issue is closed
     # https://github.com/googleapis/google-cloud-python/issues/10566
-    "google-api-core[grpc] >= 1.27.0, <3.0.0dev",
+    "google-api-core[grpc] >= 1.31.5, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.0",
     "proto-plus >= 1.15.0",
     "packaging >= 14.3",
 ]