diff --git a/CHANGELOG.md b/CHANGELOG.md
index 93015a4c8..3f84564e4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,13 @@
 [1]: https://pypi.org/project/google-cloud-pubsub/#history
 
 
+## [2.13.3](https://github.com/googleapis/python-pubsub/compare/v2.13.2...v2.13.3) (2022-07-13)
+
+
+### Bug Fixes
+
+* **deps:** require google-api-core>=1.32.0,>=2.8.0 ([#735](https://github.com/googleapis/python-pubsub/issues/735)) ([a5624fb](https://github.com/googleapis/python-pubsub/commit/a5624fbee2951c7f0c3e413d7d399a41fa0aa4bf))
+
 ## [2.13.2](https://github.com/googleapis/python-pubsub/compare/v2.13.1...v2.13.2) (2022-07-08)
 
 
diff --git a/samples/snippets/requirements-test.txt b/samples/snippets/requirements-test.txt
index ce45323b7..41002ca45 100644
--- a/samples/snippets/requirements-test.txt
+++ b/samples/snippets/requirements-test.txt
@@ -1,4 +1,4 @@
-backoff==2.0.1
+backoff==2.1.2
 pytest==7.1.2
 mock==4.0.3
 flaky==3.7.0
diff --git a/setup.py b/setup.py
index 507a5fb84..491f19840 100644
--- a/setup.py
+++ b/setup.py
@@ -22,7 +22,7 @@
 
 name = "google-cloud-pubsub"
 description = "Google Cloud Pub/Sub API client library"
-version = "2.13.2"
+version = "2.13.3"
 # Should be one of:
 # 'Development Status :: 3 - Alpha'
 # 'Development Status :: 4 - Beta'
@@ -30,7 +30,7 @@
 release_status = "Development Status :: 5 - Production/Stable"
 dependencies = [
     "grpcio >= 1.38.1, < 2.0dev",  # https://github.com/googleapis/python-pubsub/issues/414
-    "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",
     "grpc-google-iam-v1 >=0.12.4, <1.0.0dev",
diff --git a/testing/constraints-3.7.txt b/testing/constraints-3.7.txt
index 90fcc601c..38e0f719d 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
 grpcio==1.38.1
-google-api-core==2.8.0
+google-api-core==1.32.0
 libcst==0.3.10
 proto-plus==1.15.0
 grpc-google-iam-v1==0.12.4