diff --git a/.travis.yml b/.travis.yml
index b6faca4b9..2077f6af7 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -20,6 +20,9 @@ matrix:
   - python: 2.7
     env: TOX_ENV=py27
 
+  - python: 2.7
+    env: TOX_ENV=py27-old
+
   - python: 2.7
     env: TOX_ENV=py27-postgres TRIAL_FLAGS="-j 4"
     services:
diff --git a/changelog.d/3952.misc b/changelog.d/3952.misc
new file mode 100644
index 000000000..015e4a43e
--- /dev/null
+++ b/changelog.d/3952.misc
@@ -0,0 +1 @@
+Run the test suite on the oldest supported versions of our dependencies in CI.
\ No newline at end of file
diff --git a/synapse/python_dependencies.py b/synapse/python_dependencies.py
index c779f69fa..0f339a032 100644
--- a/synapse/python_dependencies.py
+++ b/synapse/python_dependencies.py
@@ -33,31 +33,32 @@ logger = logging.getLogger(__name__)
 # [2] https://setuptools.readthedocs.io/en/latest/setuptools.html#declaring-dependencies
 REQUIREMENTS = {
     "jsonschema>=2.5.1": ["jsonschema>=2.5.1"],
-    "frozendict>=0.4": ["frozendict"],
+    "frozendict>=1": ["frozendict"],
     "unpaddedbase64>=1.1.0": ["unpaddedbase64>=1.1.0"],
     "canonicaljson>=1.1.3": ["canonicaljson>=1.1.3"],
     "signedjson>=1.0.0": ["signedjson>=1.0.0"],
     "pynacl>=1.2.1": ["nacl>=1.2.1", "nacl.bindings"],
-    "service_identity>=1.0.0": ["service_identity>=1.0.0"],
+    "service_identity>=16.0.0": ["service_identity>=16.0.0"],
     "Twisted>=17.1.0": ["twisted>=17.1.0"],
     "treq>=15.1": ["treq>=15.1"],
 
     # Twisted has required pyopenssl 16.0 since about Twisted 16.6.
     "pyopenssl>=16.0.0": ["OpenSSL>=16.0.0"],
 
-    "pyyaml": ["yaml"],
-    "pyasn1": ["pyasn1"],
-    "daemonize": ["daemonize"],
-    "bcrypt": ["bcrypt>=3.1.0"],
-    "pillow": ["PIL"],
-    "pydenticon": ["pydenticon"],
-    "sortedcontainers": ["sortedcontainers"],
-    "pysaml2>=3.0.0": ["saml2>=3.0.0"],
-    "pymacaroons-pynacl": ["pymacaroons"],
+    "pyyaml>=3.11": ["yaml"],
+    "pyasn1>=0.1.9": ["pyasn1"],
+    "pyasn1-modules>=0.0.7": ["pyasn1_modules"],
+    "daemonize>=2.3.1": ["daemonize"],
+    "bcrypt>=3.1.0": ["bcrypt>=3.1.0"],
+    "pillow>=3.1.2": ["PIL"],
+    "pydenticon>=0.2": ["pydenticon"],
+    "sortedcontainers>=1.4.4": ["sortedcontainers"],
+    "pysaml2>=3.0.0": ["saml2"],
+    "pymacaroons-pynacl>=0.9.3": ["pymacaroons"],
     "msgpack-python>=0.3.0": ["msgpack"],
     "phonenumbers>=8.2.0": ["phonenumbers"],
-    "six": ["six"],
-    "prometheus_client": ["prometheus_client"],
+    "six>=1.10": ["six"],
+    "prometheus_client>=0.0.18": ["prometheus_client"],
 
     # we use attr.s(slots), which arrived in 16.0.0
     "attrs>=16.0.0": ["attr>=16.0.0"],
diff --git a/tox.ini b/tox.ini
index e4db563b4..87b5e4782 100644
--- a/tox.ini
+++ b/tox.ini
@@ -64,6 +64,26 @@ setenv =
     {[base]setenv}
     SYNAPSE_POSTGRES = 1
 
+# A test suite for the oldest supported versions of Python libraries, to catch
+# any uses of APIs not available in them.
+[testenv:py27-old]
+skip_install=True
+deps =
+    # Old automat version for Twisted
+    Automat == 0.3.0
+
+    mock
+    lxml
+commands =
+    /usr/bin/find "{toxinidir}" -name '*.pyc' -delete
+    # Make all greater-thans equals so we test the oldest version of our direct
+    # dependencies, but make the pyopenssl 17.0, which can work against an
+    # OpenSSL 1.1 compiled cryptography (as older ones don't compile on Travis).
+    /bin/sh -c 'python -m synapse.python_dependencies | sed -e "s/>=/==/g" -e "s/psycopg2==2.6//" -e "s/pyopenssl==16.0.0/pyopenssl==17.0.0/" | xargs pip install'
+    # Install Synapse itself. This won't update any libraries.
+    pip install -e .
+    {envbindir}/trial {env:TRIAL_FLAGS:} {posargs:tests} {env:TOXSUFFIX:}
+
 [testenv:py35]
 usedevelop=true