diff --git a/noxfile.py b/noxfile.py
index 4d37cd3..c5821ef 100644
--- a/noxfile.py
+++ b/noxfile.py
@@ -55,7 +55,7 @@ def lint(session):
     Returns a failure if the linters find linting errors or sufficiently
     serious code quality issues.
     """
-    session.install("flake8", BLACK_VERSION)
+    session.install("flake8", BLACK_VERSION, "click<8.1.0")
     session.run(
         "black", "--check", *BLACK_PATHS,
     )
@@ -72,7 +72,7 @@ def blacken(session):
     That run uses an image that doesn't have 3.6 installed. Before updating this
     check the state of the `gcp_ubuntu_config` we use for that Kokoro run.
     """
-    session.install(BLACK_VERSION)
+    session.install(BLACK_VERSION, "click<8.1.0")
     session.run(
         "black", *BLACK_PATHS,
     )
diff --git a/setup.py b/setup.py
index 2774b2e..c326ba5 100644
--- a/setup.py
+++ b/setup.py
@@ -40,7 +40,7 @@
     platforms="Posix; MacOS X; Windows",
     include_package_data=True,
     install_requires=(
-        "google-api-core[grpc] >= 1.22.2, < 2.0.0dev",
+        "google-api-core[grpc] >= 1.31.5, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.0",
         "libcst >= 0.2.5",
         "proto-plus >= 1.4.0",
     ),
diff --git a/testing/constraints-3.6.txt b/testing/constraints-3.6.txt
index c933887..da58b15 100644
--- a/testing/constraints-3.6.txt
+++ b/testing/constraints-3.6.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==1.22.2
+google-api-core==1.31.5
 libcst==0.2.5
-proto-plus==1.4.0
\ No newline at end of file
+proto-plus==1.4.0