diff --git a/swh/core/api/tests/__init__.py b/swh/core/api/tests/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/swh/core/tests/server_testing.py b/swh/core/api/tests/server_testing.py
similarity index 100%
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
similarity index 100%
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
similarity index 100%
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
index 0000000..e69de29
diff --git a/swh/core/tests/conftest.py b/swh/core/db/tests/conftest.py
similarity index 100%
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
similarity index 100%
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
similarity index 98%
rename from swh/core/tests/test_db.py
rename to swh/core/db/tests/test_db.py
index a9c70e8..355a384 100644
--- a/swh/core/tests/test_db.py
+++ b/swh/core/db/tests/test_db.py
@@ -1,102 +1,102 @@
 # Copyright (C) 2019  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
 import os.path
 import tempfile
 import unittest
 
 from hypothesis import strategies, given
 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,
 )
 
 
 INIT_SQL = '''
 create table test_table
 (
     i       int,
     txt     text,
     bytes   bytea
 );
 '''
 
 db_rows = strategies.lists(strategies.tuples(
     strategies.integers(-2147483648, +2147483647),
     strategies.text(
         alphabet=strategies.characters(
             blacklist_categories=['Cs'],  # surrogates
             blacklist_characters=[
                 '\x00',  # pgsql does not support the null codepoint
                 '\r',  # pgsql normalizes those
             ]
         ),
     ),
     strategies.binary(),
 ))
 
 
 @pytest.mark.db
 def test_connect():
     db_name = db_create('test-db2', dumps=[])
     try:
         db = BaseDb.connect('dbname=%s' % db_name)
         with db.cursor() as cur:
             cur.execute(INIT_SQL)
             cur.execute("insert into test_table values (1, %s, %s);",
                         ('foo', b'bar'))
             cur.execute("select * from test_table;")
             assert list(cur) == [(1, 'foo', b'bar')]
     finally:
         db_close(db.conn)
         db_destroy(db_name)
 
 
 @pytest.mark.db
 class TestDb(SingleDbTestFixture, unittest.TestCase):
     TEST_DB_NAME = 'test-db'
 
     @classmethod
     def setUpClass(cls):
         with tempfile.TemporaryDirectory() as td:
             with open(os.path.join(td, 'init.sql'), 'a') as fd:
                 fd.write(INIT_SQL)
 
             cls.TEST_DB_DUMP = os.path.join(td, '*.sql')
 
             super().setUpClass()
 
     def setUp(self):
         super().setUp()
         self.db = BaseDb(self.conn)
 
     def test_initialized(self):
         cur = self.db.cursor()
         cur.execute("insert into test_table values (1, %s, %s);",
                     ('foo', b'bar'))
         cur.execute("select * from test_table;")
         self.assertEqual(list(cur), [(1, 'foo', b'bar')])
 
     def test_reset_tables(self):
         cur = self.db.cursor()
         cur.execute("insert into test_table values (1, %s, %s);",
                     ('foo', b'bar'))
         self.reset_db_tables('test-db')
         cur.execute("select * from test_table;")
         self.assertEqual(list(cur), [])
 
     @given(db_rows)
     def test_copy_to(self, data):
         # the table is not reset between runs by hypothesis
         self.reset_db_tables('test-db')
 
         items = [dict(zip(['i', 'txt', 'bytes'], item)) for item in data]
         self.db.copy_to(items, 'test_table', ['i', 'txt', 'bytes'])
 
         cur = self.db.cursor()
         cur.execute('select * from test_table;')
         self.assertCountEqual(list(cur), data)
diff --git a/tox.ini b/tox.ini
index 71a8504..586c09b 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,26 +1,44 @@
 [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
 deps =
   flake8
 commands =
   {envpython} -m flake8