diff --git a/.travis.yml b/.travis.yml
index b566d0b..70479a9 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -25,40 +25,56 @@
         "python": "3.6"
       },
       {
-        "env": "BUILD=test DAV_SERVER=radicale REQUIREMENTS=release ",
+        "env": "BUILD=test REQUIREMENTS=release",
         "python": "3.5"
       },
       {
-        "env": "BUILD=test DAV_SERVER=xandikos REQUIREMENTS=release ",
+        "env": "BUILD=test-storage DAV_SERVER=radicale REQUIREMENTS=release ",
         "python": "3.5"
       },
       {
-        "env": "BUILD=test DAV_SERVER=radicale REQUIREMENTS=minimal ",
+        "env": "BUILD=test-storage DAV_SERVER=xandikos REQUIREMENTS=release ",
         "python": "3.5"
       },
       {
-        "env": "BUILD=test DAV_SERVER=xandikos REQUIREMENTS=minimal ",
+        "env": "BUILD=test REQUIREMENTS=minimal",
         "python": "3.5"
       },
       {
-        "env": "BUILD=test DAV_SERVER=radicale REQUIREMENTS=release ",
+        "env": "BUILD=test-storage DAV_SERVER=radicale REQUIREMENTS=minimal ",
+        "python": "3.5"
+      },
+      {
+        "env": "BUILD=test-storage DAV_SERVER=xandikos REQUIREMENTS=minimal ",
+        "python": "3.5"
+      },
+      {
+        "env": "BUILD=test REQUIREMENTS=release",
         "python": "3.6"
       },
       {
-        "env": "BUILD=test DAV_SERVER=xandikos REQUIREMENTS=release ",
+        "env": "BUILD=test-storage DAV_SERVER=radicale REQUIREMENTS=release ",
         "python": "3.6"
       },
       {
-        "env": "BUILD=test DAV_SERVER=fastmail REQUIREMENTS=release ",
+        "env": "BUILD=test-storage DAV_SERVER=xandikos REQUIREMENTS=release ",
+        "python": "3.6"
+      },
+      {
+        "env": "BUILD=test-storage DAV_SERVER=fastmail REQUIREMENTS=release ",
         "if": "NOT (type IN (pull_request))",
         "python": "3.6"
       },
       {
-        "env": "BUILD=test DAV_SERVER=radicale REQUIREMENTS=minimal ",
+        "env": "BUILD=test REQUIREMENTS=minimal",
         "python": "3.6"
       },
       {
-        "env": "BUILD=test DAV_SERVER=xandikos REQUIREMENTS=minimal ",
+        "env": "BUILD=test-storage DAV_SERVER=radicale REQUIREMENTS=minimal ",
+        "python": "3.6"
+      },
+      {
+        "env": "BUILD=test-storage DAV_SERVER=xandikos REQUIREMENTS=minimal ",
         "python": "3.6"
       },
       {
diff --git a/Makefile b/Makefile
index bbbceeb..27bbb63 100644
--- a/Makefile
+++ b/Makefile
@@ -46,14 +46,16 @@ export TESTSERVER_BASE := ./tests/storage/servers/
 CODECOV_PATH = /tmp/codecov.sh
 
 ifeq ($(CI), true)
+test-storage:
+	curl -s https://codecov.io/bash > $(CODECOV_PATH)
+	$(PYTEST) tests/storage/
+	bash $(CODECOV_PATH) -c -F storage
 test:
 	curl -s https://codecov.io/bash > $(CODECOV_PATH)
 	$(PYTEST) tests/unit/
 	bash $(CODECOV_PATH) -c -F unit
 	$(PYTEST) tests/system/
 	bash $(CODECOV_PATH) -c -F system
-	$(PYTEST) tests/storage/
-	bash $(CODECOV_PATH) -c -F storage
 else
 test:
 	$(PYTEST)
@@ -81,6 +83,10 @@ install-test: install-servers install-dev
 	fi
 	[ -z "$(TEST_EXTRA_PACKAGES)" ] || pip install $(TEST_EXTRA_PACKAGES)
 
+install-test-storage: install-test
+	# This is just an alias
+	true
+
 install-style: install-docs install-dev
 	pip install -U flake8 flake8-import-order flake8-bugbear
 
diff --git a/scripts/make_travisconf.py b/scripts/make_travisconf.py
index 6250462..56025ad 100644
--- a/scripts/make_travisconf.py
+++ b/scripts/make_travisconf.py
@@ -45,13 +45,18 @@ for python, requirements in itertools.product(
 ):
     dav_servers = ("radicale", "xandikos")
 
+    matrix.append({
+        'python': python,
+        'env': f"BUILD=test REQUIREMENTS={requirements}",
+    })
+
     if python == latest_python and requirements == "release":
         dav_servers += ("fastmail",)
 
     for dav_server in dav_servers:
         job = {
             'python': python,
-            'env': ("BUILD=test "
+            'env': ("BUILD=test-storage "
                     "DAV_SERVER={dav_server} "
                     "REQUIREMENTS={requirements} "
                     .format(dav_server=dav_server,