diff --git a/tox.ini b/tox.ini
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist=black,flake8,mypy,py3,identify
+envlist=black,flake8,mypy,py3,identify,identify-base
 
 [testenv]
 extras =
@@ -21,6 +21,25 @@
 commands =
   pytest {envsitepackagesdir}/swh/model/tests/test_cli.py
 
+[testenv:identify-base]
+# Tests swh-identify works even with the bare minimum of dependencies install
+# (eg. no dulwich)
+extras =
+deps =
+  Click
+  pytest
+commands =
+  # Run all tests that don't depend on dulwich:
+  pytest {envsitepackagesdir}/swh/model/tests/test_cli.py -k 'not snapshot'
+  # Check we get a nice error if we depend on dulwich:
+  /usr/bin/env bash -c " \
+    # run swh-identify, should have non-zero exit code (ie. error)
+    ! swh-identify -t snapshot . 2>&1 \
+    # check the output contains the error message
+    | (! grep 'Dulwich package') \
+    > /dev/null \
+  "
+
 [testenv:black]
 skip_install = true
 deps =