diff --git a/changelog.d/5675.doc b/changelog.d/5675.doc
new file mode 100644
index 0000000000..4cd4d0be1a
--- /dev/null
+++ b/changelog.d/5675.doc
@@ -0,0 +1 @@
+Minor tweaks to postgres documentation.
diff --git a/debian/changelog b/debian/changelog
index b964cf90a2..8aba444f1d 100644
--- a/debian/changelog
+++ b/debian/changelog
@@ -3,6 +3,9 @@ matrix-synapse-py3 (1.1.0-1) UNRELEASED; urgency=medium
   [ Amber Brown ]
   * Update logging config defaults to match API changes in Synapse.
 
+  [ Richard van der Hoff ]
+  * Add Recommends and Depends for some libraries which you probably want.
+
  -- Erik Johnston <erikj@rae>  Thu, 04 Jul 2019 13:59:02 +0100
 
 matrix-synapse-py3 (1.1.0) stable; urgency=medium
diff --git a/debian/control b/debian/control
index 4abfa02051..9e679c9d42 100644
--- a/debian/control
+++ b/debian/control
@@ -2,16 +2,20 @@ Source: matrix-synapse-py3
 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.
 Build-Depends:
  debhelper (>= 9),
  dh-systemd,
  dh-virtualenv (>= 1.1),
+ libsystemd-dev,
+ libpq-dev,
  lsb-release,
  python3-dev,
  python3,
  python3-setuptools,
  python3-pip,
  python3-venv,
+ libsqlite3-dev,
  tar,
 Standards-Version: 3.9.8
 Homepage: https://github.com/matrix-org/synapse
@@ -28,9 +32,12 @@ Depends:
  debconf,
  python3-distutils|libpython3-stdlib (<< 3.6),
  ${misc:Depends},
+ ${shlibs:Depends},
  ${synapse:pydepends},
 # some of our scripts use perl, but none of them are important,
 # so we put perl:Depends in Suggests rather than Depends.
+Recommends:
+ ${shlibs1:Recommends},
 Suggests:
  sqlite3,
  ${perl:Depends},
diff --git a/debian/rules b/debian/rules
index 05cbbdde08..a4d2ce2ba4 100755
--- a/debian/rules
+++ b/debian/rules
@@ -3,15 +3,29 @@
 # Build Debian package using https://github.com/spotify/dh-virtualenv
 #
 
+# assume we only have one package
+PACKAGE_NAME:=`dh_listpackages`
+
 override_dh_systemd_enable:
 	dh_systemd_enable --name=matrix-synapse
 
 override_dh_installinit:
 	dh_installinit --name=matrix-synapse
 
+# we don't really want to strip the symbols from our object files.
 override_dh_strip:
 
 override_dh_shlibdeps:
+        # make the postgres package's dependencies a recommendation
+        # rather than a hard dependency.
+	find debian/$(PACKAGE_NAME)/ -path '*/site-packages/psycopg2/*.so' | \
+	    xargs dpkg-shlibdeps -Tdebian/$(PACKAGE_NAME).substvars \
+	        -pshlibs1 -dRecommends
+
+        # all the other dependencies can be normal 'Depends' requirements,
+        # except for PIL's, which is self-contained and which confuses
+        # dpkg-shlibdeps.
+	dh_shlibdeps -X site-packages/PIL/.libs -X site-packages/psycopg2
 
 override_dh_virtualenv:
 	./debian/build_virtualenv
diff --git a/docker/Dockerfile-dhvirtualenv b/docker/Dockerfile-dhvirtualenv
index ceedbad68a..0117ab8bcc 100644
--- a/docker/Dockerfile-dhvirtualenv
+++ b/docker/Dockerfile-dhvirtualenv
@@ -43,6 +43,9 @@ RUN cd dh-virtualenv-1.1 && dpkg-buildpackage -us -uc -b
 FROM ${distro}
 
 # Install the build dependencies
+#
+# NB: keep this list in sync with the list of build-deps in debian/control
+# TODO: it would be nice to do that automatically.
 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 \
diff --git a/docs/postgres.rst b/docs/postgres.rst
index 0ae52ccbd8..e08a5116b9 100644
--- a/docs/postgres.rst
+++ b/docs/postgres.rst
@@ -11,7 +11,9 @@ a postgres database.
 
 * If you are using the `matrix.org debian/ubuntu
   packages <../INSTALL.md#matrixorg-packages>`_,
-  the necessary libraries will already be installed.
+  the necessary python library will already be installed, but you will need to
+  ensure the low-level postgres library is installed, which you can do with
+  ``apt install libpq5``.
 
 * For other pre-built packages, please consult the documentation from the
   relevant package.
@@ -34,7 +36,7 @@ Assuming your PostgreSQL database user is called ``postgres``, create a user
    su - postgres
    createuser --pwprompt synapse_user
 
-Before you can authenticate with the ``synapse_user``, you must create a 
+Before you can authenticate with the ``synapse_user``, you must create a
 database that it can access. To create a database, first connect to the database
 with your database user::
 
@@ -53,7 +55,7 @@ and then run::
 This would create an appropriate database named ``synapse`` owned by the
 ``synapse_user`` user (which must already have been created as above).
 
-Note that the PostgreSQL database *must* have the correct encoding set (as 
+Note that the PostgreSQL database *must* have the correct encoding set (as
 shown above), otherwise it will not be able to store UTF8 strings.
 
 You may need to enable password authentication so ``synapse_user`` can connect