diff --git a/setup.py b/setup.py
index 37bb670..2da8c97 100644
--- a/setup.py
+++ b/setup.py
@@ -45,7 +45,7 @@
     platforms="Posix; MacOS X; Windows",
     include_package_data=True,
     install_requires=(
-        "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 b66105b..317c02d 100644
--- a/testing/constraints-3.7.txt
+++ b/testing/constraints-3.7.txt
@@ -5,6 +5,6 @@
 #
 # 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
 protobuf==3.19.0