diff --git a/setup.py b/setup.py
index 2350653b..0b6fc74f 100644
--- a/setup.py
+++ b/setup.py
@@ -39,8 +39,9 @@
     # Until this issue is closed
     # https://github.com/googleapis/google-cloud-python/issues/10566
     "google-cloud-core >= 1.4.1, <3.0.0dev",
-    "grpc-google-iam-v1 >= 0.12.3, < 0.13dev",
-    "proto-plus >= 1.15.0",
+    "grpc-google-iam-v1 >=0.12.4, <1.0.0dev",
+    "proto-plus >= 1.15.0, <2.0.0dev",
+    "protobuf >= 3.19.0, <4.0.0dev",
 ]
 extras = {}
 
diff --git a/testing/constraints-3.6.txt b/testing/constraints-3.6.txt
index 0aa01664..415307c5 100644
--- a/testing/constraints-3.6.txt
+++ b/testing/constraints-3.6.txt
@@ -8,3 +8,4 @@
 google-api-core==1.31.5
 google-cloud-core==1.4.1
 proto-plus==1.15.0
+protobuf==3.19.0