diff --git a/.buildkite/dagster-buildkite/dagster_buildkite/steps/dagster.py b/.buildkite/dagster-buildkite/dagster_buildkite/steps/dagster.py
--- a/.buildkite/dagster-buildkite/dagster_buildkite/steps/dagster.py
+++ b/.buildkite/dagster-buildkite/dagster_buildkite/steps/dagster.py
@@ -275,6 +275,7 @@
     ModuleBuildSpec(
         "python_modules/dagster-graphql",
         tox_env_suffixes=[
+            "-not_graphql_context_test_suite",
             "-in_memory_instance_hosted_user_process_env",
             "-in_memory_instance_multi_location",
             "-in_memory_instance_managed_grpc_env",
@@ -292,7 +293,7 @@
         tox_file="tox_postgres.ini",
         buildkite_label="dagster-graphql-postgres",
         tox_env_suffixes=[
-            "-not_graphql_context_test_suite",
+            "-variant",
             "-postgres_instance_hosted_user_process_env",
             "-postgres_instance_multi_location",
             "-postgres_instance_managed_grpc_env",
diff --git a/python_modules/dagster-graphql/dagster_graphql_tests/graphql/test_graphql_context_test_suite.py b/python_modules/dagster-graphql/dagster_graphql_tests/graphql/test_graphql_context_test_suite.py
--- a/python_modules/dagster-graphql/dagster_graphql_tests/graphql/test_graphql_context_test_suite.py
+++ b/python_modules/dagster-graphql/dagster_graphql_tests/graphql/test_graphql_context_test_suite.py
@@ -8,8 +8,11 @@
 from .graphql_context_test_suite import GraphQLContextVariant, manage_graphql_context
 
 
+@pytest.mark.variant
 @pytest.mark.parametrize("variant", GraphQLContextVariant.all_readonly_variants())
 def test_readonly_variants(variant):
+    # Note: This mark is only run in the `tox_postgres.ini` file and not the default `tox.ini`
+    # file because 3 of the variants have a postgres dependency
     assert isinstance(variant, GraphQLContextVariant)
     with manage_graphql_context(variant) as context:
         assert isinstance(context.instance.run_launcher, ExplodingRunLauncher)
diff --git a/python_modules/dagster-graphql/pytest.ini b/python_modules/dagster-graphql/pytest.ini
--- a/python_modules/dagster-graphql/pytest.ini
+++ b/python_modules/dagster-graphql/pytest.ini
@@ -1,5 +1,6 @@
 [pytest]
 markers =
+    variant:
     in_memory_instance: Uses an in-memory instance.
     sqlite_instance: Uses a sqlite instance.
     postgres_instance: Uses a postgres instance.
diff --git a/python_modules/dagster-graphql/tox.ini b/python_modules/dagster-graphql/tox.ini
--- a/python_modules/dagster-graphql/tox.ini
+++ b/python_modules/dagster-graphql/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py{38,37,36,27}-{unix,windows}-{in_memory_instance_hosted_user_process_env,in_memory_instance_multi_location,sqlite_instance_multi_location,in_memory_instance_managed_grpc_env,sqlite_instance_managed_grpc_env,sqlite_instance_deployed_grpc_env},pylint
+envlist = py{38,37,36,27}-{unix,windows}-{not_graphql_context_test_suite,in_memory_instance_hosted_user_process_env,in_memory_instance_multi_location,sqlite_instance_multi_location,in_memory_instance_managed_grpc_env,sqlite_instance_managed_grpc_env,sqlite_instance_deployed_grpc_env},pylint
 
 
 [testenv]
@@ -15,6 +15,7 @@
   !windows: /bin/bash -c '! pip list --exclude-editable | grep -e dagster -e dagit'
   coverage erase
   echo -e "--- \033[0;32m:pytest: Running tox tests\033[0m"
+  not_graphql_context_test_suite: pytest -m "not graphql_context_test_suite and not variant" -vv --junitxml=dagster_graphql_test_results.xml --cov=dagster_graphql --cov-append --cov-report= {posargs}
   in_memory_instance_hosted_user_process_env: pytest -m "graphql_context_test_suite and in_memory_instance and hosted_user_process_env" -vv --junitxml=dagster_graphql_test_results.xml --cov=dagster_graphql --cov-append --cov-report= {posargs}
   in_memory_instance_multi_location: pytest -m "graphql_context_test_suite and in_memory_instance and multi_location" -vv --junitxml=dagster_graphql_test_results.xml --cov=dagster_graphql --cov-append --cov-report= {posargs}
   in_memory_instance_managed_grpc_env: pytest -m "graphql_context_test_suite and in_memory_instance and managed_grpc_env" -vv --junitxml=dagster_graphql_test_results.xml --cov=dagster_graphql --cov-append --cov-report= {posargs}
diff --git a/python_modules/dagster-graphql/tox_postgres.ini b/python_modules/dagster-graphql/tox_postgres.ini
--- a/python_modules/dagster-graphql/tox_postgres.ini
+++ b/python_modules/dagster-graphql/tox_postgres.ini
@@ -14,7 +14,6 @@
 commands =
   !windows: /bin/bash -c '! pip list --exclude-editable | grep -e dagster -e dagit'
   echo -e "--- \033[0;32m:pytest: Running tox tests\033[0m"
-  not_graphql_context_test_suite: pytest -m "not graphql_context_test_suite" -vv --junitxml=dagster_graphql_test_results.xml --cov=dagster_graphql --cov-append --cov-report= {posargs}
   postgres_instance_hosted_user_process_env: pytest -m "graphql_context_test_suite and postgres_instance and hosted_user_process_env" -vv --junitxml=dagster_graphql_test_results.xml --cov=dagster_graphql --cov-append --cov-report= {posargs}
   postgres_instance_multi_location: pytest -m "graphql_context_test_suite and postgres_instance and multi_location" -vv --junitxml=dagster_graphql_test_results.xml --cov=dagster_graphql --cov-append --cov-report= {posargs}
   postgres_instance_managed_grpc_env: pytest -m "graphql_context_test_suite and postgres_instance and managed_grpc_env" -vv --junitxml=dagster_graphql_test_results.xml --cov=dagster_graphql --cov-append --cov-report= {posargs}