diff --git a/requirements.txt b/requirements.txt
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,13 +1,3 @@
 PyYAML
 systemd-python
 
-# these deps below are now handled in dedicated 'extras' and should be removed
-# from this main requirement file ASAP
-arrow
-aiohttp
-msgpack > 0.5
-psycopg2
-python-dateutil
-requests
-Flask
-decorator
diff --git a/swh/core/api/tests/__init__.py b/swh/core/api/tests/__init__.py
new file mode 100644
diff --git a/swh/core/tests/server_testing.py b/swh/core/api/tests/server_testing.py
rename from swh/core/tests/server_testing.py
rename to swh/core/api/tests/server_testing.py
diff --git a/swh/core/tests/test_api.py b/swh/core/api/tests/test_api.py
rename from swh/core/tests/test_api.py
rename to swh/core/api/tests/test_api.py
diff --git a/swh/core/tests/test_serializers.py b/swh/core/api/tests/test_serializers.py
rename from swh/core/tests/test_serializers.py
rename to swh/core/api/tests/test_serializers.py
diff --git a/swh/core/db/tests/__init__.py b/swh/core/db/tests/__init__.py
new file mode 100644
diff --git a/swh/core/tests/conftest.py b/swh/core/db/tests/conftest.py
rename from swh/core/tests/conftest.py
rename to swh/core/db/tests/conftest.py
diff --git a/swh/core/tests/db_testing.py b/swh/core/db/tests/db_testing.py
rename from swh/core/tests/db_testing.py
rename to swh/core/db/tests/db_testing.py
diff --git a/swh/core/tests/test_db.py b/swh/core/db/tests/test_db.py
rename from swh/core/tests/test_db.py
rename to swh/core/db/tests/test_db.py
--- a/swh/core/tests/test_db.py
+++ b/swh/core/db/tests/test_db.py
@@ -11,7 +11,7 @@
 import pytest
 
 from swh.core.db import BaseDb
-from swh.core.tests.db_testing import (
+from .db_testing import (
     SingleDbTestFixture, db_create, db_destroy, db_close,
 )
 
diff --git a/tox.ini b/tox.ini
--- a/tox.ini
+++ b/tox.ini
@@ -1,22 +1,40 @@
 [tox]
-envlist=flake8,py3
+envlist=flake8,py3-{core,db,server}
 
-[testenv:py3]
+[testenv:py3-core]
 deps =
-  .[testing]
-  pytest-cov
+  -rrequirements-test.txt
+  .
+commands =
+  pytest --doctest-modules swh/core/tests {posargs}
+
+[testenv:py3-db]
+deps =
+  -rrequirements-test.txt
+  .[db]
   pifpaf
 commands =
-  pifpaf run postgresql -- pytest --doctest-modules --hypothesis-profile=fast --cov=swh --cov-branch {posargs}
+  pifpaf run postgresql -- \
+    pytest swh/core/db/tests {posargs}
 
-[testenv:py3-slow]
+[testenv:py3-server]
+deps =
+  -rrequirements-test.txt
+  .[http]
+commands =
+  pytest swh/core/api/tests {posargs}
+
+[testenv:py3]
 deps =
   .[testing]
   pytest-cov
   pifpaf
 commands =
-  pifpaf run postgresql -- pytest --doctest-modules --hypothesis-profile=slow --cov=swh --cov-branch {posargs}
-
+  pifpaf run postgresql -- \
+    pytest --doctest-modules \
+	       --hypothesis-profile=slow \
+	       --cov=swh --cov-branch \
+		   {posargs}
 
 [testenv:flake8]
 skip_install = true