diff --git a/packages/google-cloud-iam-logging/setup.py b/packages/google-cloud-iam-logging/setup.py
index 16ce493f47ed..e7c5cecbf896 100644
--- a/packages/google-cloud-iam-logging/setup.py
+++ b/packages/google-cloud-iam-logging/setup.py
@@ -41,7 +41,7 @@
         # 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] >= 1.22.2, < 3.0.0dev",
+        "google-api-core[grpc] >= 1.31.5, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.0",
         "proto-plus >= 1.15.0",
         "packaging >= 14.3",
         "grpc-google-iam-v1 >= 0.12.3, < 0.13dev",
diff --git a/packages/google-cloud-iam-logging/testing/constraints-3.6.txt b/packages/google-cloud-iam-logging/testing/constraints-3.6.txt
index 2187f5ecaa51..77421a54e5b2 100644
--- a/packages/google-cloud-iam-logging/testing/constraints-3.6.txt
+++ b/packages/google-cloud-iam-logging/testing/constraints-3.6.txt
@@ -5,8 +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==1.22.2
+google-api-core==1.31.5
 proto-plus==1.15.0
 packaging==14.3
 grpc-google-iam-v1==0.12.3
-google-auth==1.24.0  # TODO: remove once google-auth>=1.25.0 is required transitively through google-api-core