diff --git a/packages/google-cloud-appengine-logging/setup.py b/packages/google-cloud-appengine-logging/setup.py
index d5d2d27aeef3..c983024d76a6 100644
--- a/packages/google-cloud-appengine-logging/setup.py
+++ b/packages/google-cloud-appengine-logging/setup.py
@@ -45,7 +45,7 @@
         # 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",
     ),
diff --git a/packages/google-cloud-appengine-logging/testing/constraints-3.6.txt b/packages/google-cloud-appengine-logging/testing/constraints-3.6.txt
index a0937fcf94d7..766f28838110 100644
--- a/packages/google-cloud-appengine-logging/testing/constraints-3.6.txt
+++ b/packages/google-cloud-appengine-logging/testing/constraints-3.6.txt
@@ -5,7 +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==1.22.2
+google-api-core==1.31.5
 proto-plus==1.15.0
 packaging==14.3
-google-auth==1.24.0  # TODO: remove when google-auth>=1.25.0 is required through google-api-core