diff --git a/README.md b/README.md
index 13f8aa2f3..6e19a3888 100644
--- a/README.md
+++ b/README.md
@@ -19,9 +19,10 @@ GLib on Windows.
 
 ## Supported versions
 
-Only the most recent unstable and stable release series are supported. All
-older versions are not supported upstream and may contain bugs, some of
-which may be exploitable security vulnerabilities.
+Upstream GLib only supports the most recent stable release series, the previous
+stable release series, and the current development release series. All
+older versions are not supported upstream and may contain bugs, some of which
+may be exploitable security vulnerabilities.
 
 See [SECURITY.md](SECURITY.md) for more details.
 
diff --git a/SECURITY.md b/SECURITY.md
index c7fb8162c..c7797d5bd 100644
--- a/SECURITY.md
+++ b/SECURITY.md
@@ -7,11 +7,16 @@
 
 ## Supported Versions
 
-Upstream GLib only supports the most recent stable release series, and the
-current development release series. Any older stable release series are no
-longer supported, although they may still receive backported security updates
-in long-term support distributions. Such support is up to the distributions,
-though.
+Upstream GLib only supports the most recent stable release series, the previous
+stable release series, and the current development release series. Any older
+stable release series are no longer supported, although they may still receive
+backported security updates in long-term support distributions. Such support is
+up to the distributions, though.
+
+The previous stable release series will generally receive fixes only for high
+impact security issues, at maintainer discretion. Since such issues are rare,
+it's expected that there may be no backports or releases on the previous stable
+branch.
 
 Under GLib’s versioning scheme, stable release series have an *even* minor
 component (for example, 2.66.0, 2.66.1, 2.68.3), and development release series