diff --git a/changelog.d/10429.misc b/changelog.d/10429.misc
new file mode 100644
index 000000000..ccb2217f6
--- /dev/null
+++ b/changelog.d/10429.misc
@@ -0,0 +1 @@
+Drop backwards-compatibility code that was required to support Ubuntu Xenial.
diff --git a/debian/build_virtualenv b/debian/build_virtualenv
index 21caad90c..68c865995 100755
--- a/debian/build_virtualenv
+++ b/debian/build_virtualenv
@@ -33,13 +33,11 @@ esac
 # Use --builtin-venv to use the better `venv` module from CPython 3.4+ rather
 # than the 2/3 compatible `virtualenv`.
 
-# Pin pip to 20.3.4 to fix breakage in 21.0 on py3.5 (xenial)
-
 dh_virtualenv \
     --install-suffix "matrix-synapse" \
     --builtin-venv \
     --python "$SNAKE" \
-    --upgrade-pip-to="20.3.4" \
+    --upgrade-pip \
     --preinstall="lxml" \
     --preinstall="mock" \
     --extra-pip-arg="--no-cache-dir" \
diff --git a/debian/changelog b/debian/changelog
index 4d214c23b..55f7ee003 100644
--- a/debian/changelog
+++ b/debian/changelog
@@ -1,3 +1,9 @@
+matrix-synapse-py3 (1.39.0ubuntu1) UNRELEASED; urgency=medium
+
+  * Drop backwards-compatibility code that was required to support Ubuntu Xenial.
+
+ -- Richard van der Hoff <richard@matrix.org>  Tue, 20 Jul 2021 00:10:03 +0100
+
 matrix-synapse-py3 (1.39.0~rc1) stable; urgency=medium
 
   * New synapse release 1.39.0rc1.
diff --git a/debian/compat b/debian/compat
index ec635144f..f599e28b8 100644
--- a/debian/compat
+++ b/debian/compat
@@ -1 +1 @@
-9
+10
diff --git a/debian/control b/debian/control
index 8167a901a..763fabd6f 100644
--- a/debian/control
+++ b/debian/control
@@ -3,11 +3,8 @@ Section: contrib/python
 Priority: extra
 Maintainer: Synapse Packaging team <packages@matrix.org>
 # keep this list in sync with the build dependencies in docker/Dockerfile-dhvirtualenv.
-# TODO: Remove the dependency on dh-systemd after dropping support for Ubuntu xenial
-#       On all other supported releases, it's merely a transitional package which
-#       does nothing but depends on debhelper (> 9.20160709)
 Build-Depends:
- debhelper (>= 9.20160709) | dh-systemd,
+ debhelper (>= 10),
  dh-virtualenv (>= 1.1),
  libsystemd-dev,
  libpq-dev,
diff --git a/debian/rules b/debian/rules
index c744060a5..b9d490adc 100755
--- a/debian/rules
+++ b/debian/rules
@@ -51,7 +51,5 @@ override_dh_shlibdeps:
 override_dh_virtualenv:
 	./debian/build_virtualenv
 
-# We are restricted to compat level 9 (because xenial), so have to
-# enable the systemd bits manually.
 %:
-	dh $@ --with python-virtualenv --with systemd
+	dh $@ --with python-virtualenv
diff --git a/docker/Dockerfile-dhvirtualenv b/docker/Dockerfile-dhvirtualenv
index 0d7463037..017be8555 100644
--- a/docker/Dockerfile-dhvirtualenv
+++ b/docker/Dockerfile-dhvirtualenv
@@ -15,6 +15,15 @@ ARG distro=""
 ###
 ### Stage 0: build a dh-virtualenv
 ###
+
+# This is only really needed on bionic and focal, since other distributions we
+# care about have a recent version of dh-virtualenv by default. Unfortunately,
+# it looks like focal is going to be with us for a while.
+#
+# (focal doesn't have a dh-virtualenv package at all. There is a PPA at
+# https://launchpad.net/~jyrki-pulliainen/+archive/ubuntu/dh-virtualenv, but
+# it's not obviously easier to use that than to build our own.)
+
 FROM ${distro} as builder
 
 RUN apt-get update -qq -o Acquire::Languages=none
@@ -27,7 +36,7 @@ RUN env DEBIAN_FRONTEND=noninteractive apt-get install \
         wget
 
 # fetch and unpack the package
-# TODO: Upgrade to 1.2.2 once xenial is dropped
+# TODO: Upgrade to 1.2.2 once bionic is dropped (1.2.2 requires debhelper 12; bionic has only 11)
 RUN mkdir /dh-virtualenv
 RUN wget -q -O /dh-virtualenv.tar.gz https://github.com/spotify/dh-virtualenv/archive/ac6e1b1.tar.gz
 RUN tar -xv --strip-components=1 -C /dh-virtualenv -f /dh-virtualenv.tar.gz
@@ -59,8 +68,6 @@ ENV LANG C.UTF-8
 #
 # NB: keep this list in sync with the list of build-deps in debian/control
 # TODO: it would be nice to do that automatically.
-# TODO: Remove the dh-systemd stanza after dropping support for Ubuntu xenial
-#       it's a transitional package on all other, more recent releases
 RUN apt-get update -qq -o Acquire::Languages=none \
     && env DEBIAN_FRONTEND=noninteractive apt-get install \
         -yqq --no-install-recommends -o Dpkg::Options::=--force-unsafe-io \
@@ -76,10 +83,7 @@ RUN apt-get update -qq -o Acquire::Languages=none \
         python3-venv \
         sqlite3 \
         libpq-dev \
-        xmlsec1 \
-    && ( env DEBIAN_FRONTEND=noninteractive apt-get install \
-         -yqq --no-install-recommends -o Dpkg::Options::=--force-unsafe-io \
-         dh-systemd || true )
+        xmlsec1
 
 COPY --from=builder /dh-virtualenv_1.2~dev-1_all.deb /