diff --git a/CHANGES.md b/CHANGES.md
index f1332edf9..727275fa3 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -1,9 +1,12 @@
 Synapse 0.34.0 (2018-12-20)
 ===========================
 
-Synapse 0.34.0 is the first release to fully support Python 3. We recommend
-upgrading to Python 3, but make sure to read the
-[upgrade notes](UPGRADE.rst#upgrading-to-v0340) when doing so.
+Synapse 0.34.0 is the first release to fully support Python 3. Synapse will now
+run on Python versions 3.5 or 3.6 (as well as 2.7). Support for Python 3.7
+remains experimental.
+
+We recommend upgrading to Python 3, but make sure to read the [upgrade
+notes](UPGRADE.rst#upgrading-to-v0340) when doing so.
 
 Features
 --------
diff --git a/UPGRADE.rst b/UPGRADE.rst
index b8dead480..b214a1552 100644
--- a/UPGRADE.rst
+++ b/UPGRADE.rst
@@ -51,8 +51,9 @@ returned by the Client-Server API:
 Upgrading to v0.34.0
 ====================
 
-1. This release is the first to fully support Python 3. We recommend switching
-   to Python 3, as it has been shown to give performance improvements.
+1. This release is the first to fully support Python 3. Synapse will now run on
+   Python versions 3.5, or 3.6 (as well as 2.7). We recommend switching to
+   Python 3, as it has been shown to give performance improvements.
 
    For users who have installed Synapse into a virtualenv, we recommend doing
    this by creating a new virtualenv. For example::