diff --git a/setup.py b/setup.py
index 39649d6e28..3da9372306 100644
--- a/setup.py
+++ b/setup.py
@@ -32,13 +32,13 @@
     # 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] >= 1.26.0, <3.0.0dev",
+    "google-api-core[grpc] >= 1.31.5, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.0",
     # NOTE: Maintainers, please do not require google-cloud-core>=2.x.x
     # Until this issue is closed
     # https://github.com/googleapis/google-cloud-python/issues/10566
     "google-cloud-core >= 1.4.1, < 3.0dev",
     "grpc-google-iam-v1 >= 0.12.3, < 0.13dev",
-    "proto-plus >= 1.11.0, != 1.19.6",
+    "proto-plus >= 1.15.0, != 1.19.6",
     "sqlparse >= 0.3.0",
     "packaging >= 14.3",
 ]
diff --git a/testing/constraints-3.6.txt b/testing/constraints-3.6.txt
index 2eac9c8653..7ceb82cd99 100644
--- a/testing/constraints-3.6.txt
+++ b/testing/constraints-3.6.txt
@@ -5,11 +5,11 @@
 #
 # e.g., if setup.py has "foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have foo==1.14.0
-google-api-core==1.26.0
+google-api-core==1.31.5
 google-cloud-core==1.4.1
 grpc-google-iam-v1==0.12.3
 libcst==0.2.5
-proto-plus==1.13.0
+proto-plus==1.15.0
 sqlparse==0.3.0
 opentelemetry-api==1.1.0
 opentelemetry-sdk==1.1.0