diff --git a/debian/build_virtualenv b/debian/build_virtualenv
index 68c8659953..801ecb9086 100755
--- a/debian/build_virtualenv
+++ b/debian/build_virtualenv
@@ -100,3 +100,18 @@ esac
 # add a dependency on the right version of python to substvars.
 PYPKG=`basename $SNAKE`
 echo "synapse:pydepends=$PYPKG" >> debian/matrix-synapse-py3.substvars
+
+
+# add a couple of triggers.  This is needed so that dh-virtualenv can rebuild
+# the venv when the system python changes (see
+# https://dh-virtualenv.readthedocs.io/en/latest/tutorial.html#step-2-set-up-packaging-for-your-project)
+#
+# we do it here rather than the more conventional way of just adding it to
+# debian/matrix-synapse-py3.triggers, because we need to add a trigger on the
+# right version of python.
+cat >>"debian/.debhelper/generated/matrix-synapse-py3/triggers" <<EOF
+# triggers for dh-virtualenv
+interest-noawait $SNAKE
+interest dh-virtualenv-interpreter-update
+
+EOF
diff --git a/debian/changelog b/debian/changelog
index f0557c35ef..45df5c170b 100644
--- a/debian/changelog
+++ b/debian/changelog
@@ -2,6 +2,8 @@ matrix-synapse-py3 (1.40.0~rc1) stable; urgency=medium
 
   [ Richard van der Hoff ]
   * Drop backwards-compatibility code that was required to support Ubuntu Xenial.
+  * Update package triggers so that the virtualenv is correctly rebuilt
+    when the system python is rebuilt, on recent Python versions.
 
   [ Synapse Packaging team ]
   * New synapse release 1.40.0~rc1.
diff --git a/debian/matrix-synapse-py3.triggers b/debian/matrix-synapse-py3.triggers
deleted file mode 100644
index f8c1fdb021..0000000000
--- a/debian/matrix-synapse-py3.triggers
+++ /dev/null
@@ -1,9 +0,0 @@
-# Register interest in Python interpreter changes and
-# don't make the Python package dependent on the virtualenv package
-# processing (noawait)
-interest-noawait /usr/bin/python3.5
-interest-noawait /usr/bin/python3.6
-interest-noawait /usr/bin/python3.7
-
-# Also provide a symbolic trigger for all dh-virtualenv packages
-interest dh-virtualenv-interpreter-update