diff --git a/setup.py b/setup.py
index 86ec0a8..d02b120 100644
--- a/setup.py
+++ b/setup.py
@@ -27,7 +27,10 @@
 # 'Development Status :: 4 - Beta'
 # 'Development Status :: 5 - Production/Stable'
 release_status = "Development Status :: 4 - Beta"
-dependencies = ["google-api-core[grpc]>=1.28.0, <3.0dev", "protobuf >= 3.12.0"]
+dependencies = [
+    "google-api-core[grpc] >= 1.31.5, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.0",
+    "protobuf >= 3.12.0",
+]
 
 # Setup boilerplate below this line.
 
diff --git a/testing/constraints-3.6.txt b/testing/constraints-3.6.txt
index a59bf71..716c952 100644
--- a/testing/constraints-3.6.txt
+++ b/testing/constraints-3.6.txt
@@ -6,4 +6,4 @@
 # e.g., if setup.py has "foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have foo==1.14.0
 protobuf==3.12.0
-google-api-core==1.28.0
+google-api-core==1.31.5