diff --git a/setup.py b/setup.py
index 58cf4790..c3faa3e2 100644
--- a/setup.py
+++ b/setup.py
@@ -28,7 +28,7 @@
 # '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.*",
     "proto-plus >= 1.15.0, <2.0.0dev",
     "protobuf >= 3.19.0, <4.0.0dev",
 ]
diff --git a/testing/constraints-3.7.txt b/testing/constraints-3.7.txt
index f47a5d58..5d57a8d5 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
 proto-plus==1.15.0
 libcst==0.2.5
 protobuf==3.19.0