diff --git a/setup.py b/setup.py
index 5baaeef3b..cf4189b97 100644
--- a/setup.py
+++ b/setup.py
@@ -29,7 +29,7 @@
 # 'Development Status :: 5 - Production/Stable'
 release_status = "Development Status :: 5 - Production/Stable"
 dependencies = [
-    "google-api-core[grpc] >= 2.8.0, <3.0.0dev",
+    "google-api-core[grpc] >= 1.32.0, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.*,!=2.4.*,!=2.5.*,!=2.6.*,!=2.7.*",
     "google-cloud-appengine-logging>=0.1.0, <2.0.0dev",
     "google-cloud-audit-log >= 0.1.0, < 1.0.0dev",
     "google-cloud-core >= 2.0.0, <3.0.0dev",
diff --git a/testing/constraints-3.7.txt b/testing/constraints-3.7.txt
index 2cd939a88..07d97d4a8 100644
--- a/testing/constraints-3.7.txt
+++ b/testing/constraints-3.7.txt
@@ -5,7 +5,7 @@
 #
 # 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==2.8.0
+google-api-core==1.32.0
 google-cloud-core==2.0.0
 proto-plus==1.15.0
 protobuf==3.19.0