diff --git a/noxfile.py b/noxfile.py
index 03aa2f5..b613354 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,
     )
@@ -65,7 +65,7 @@ def lint(session):
 @nox.session(python=DEFAULT_PYTHON_VERSION)
 def blacken(session):
     """Run black. Format code to uniform standard."""
-    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 b17a656..c341521 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] >= 1.26.0, <2.0.0dev",
+        "google-api-core[grpc] >= 1.31.5, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.0",
         "proto-plus >= 1.10.0",
         "packaging >= 14.3",
         "grpc-google-iam-v1 >= 0.12.3, < 0.13dev",
diff --git a/testing/constraints-3.6.txt b/testing/constraints-3.6.txt
index bbc5a8c..0b012f8 100644
--- a/testing/constraints-3.6.txt
+++ b/testing/constraints-3.6.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
-google-api-core==1.26.0
+google-api-core==1.31.5
 proto-plus==1.10.0
 grpc-google-iam-v1==0.12.3
 packaging==14.3