diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 96767cb98..8b93687ec 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -155,9 +155,8 @@ installed-tests:
     # FIXME Install newer xdg-desktop-portal with
     # GMemoryMonitor support, see:
     # https://github.com/flatpak/xdg-desktop-portal/pull/365
-    - git clone --single-branch https://github.com/flatpak/xdg-desktop-portal.git
+    - git clone --branch 1.6.0 --depth 1 --no-tags https://github.com/flatpak/xdg-desktop-portal.git
     - cd xdg-desktop-portal
-    - git reset --hard 1.6.0
     - ./autogen.sh --prefix=/usr --libdir=/usr/lib64 --disable-libportal --disable-dependency-tracking
     - make
     - sudo make install
@@ -165,7 +164,7 @@ installed-tests:
     # FIXME install newer gobject-introspection
     # with GMemoryMonitor support, see:
     # https://gitlab.gnome.org/GNOME/gobject-introspection/merge_requests/193
-    - git clone --single-branch https://gitlab.gnome.org/GNOME/gobject-introspection.git
+    - git clone --branch master --depth 1 --no-tags https://gitlab.gnome.org/GNOME/gobject-introspection.git
     - cd gobject-introspection
     - /usr/bin/meson _build --prefix=/usr --libdir=/usr/lib64
     - ninja -C _build
diff --git a/.gitlab-ci/cache-subprojects.sh b/.gitlab-ci/cache-subprojects.sh
index 421631ed2..fb0b1df82 100755
--- a/.gitlab-ci/cache-subprojects.sh
+++ b/.gitlab-ci/cache-subprojects.sh
@@ -2,7 +2,7 @@
 
 set -e
 
-git clone https://gitlab.gnome.org/GNOME/glib.git
+git clone --depth 1 --no-tags https://gitlab.gnome.org/GNOME/glib.git
 meson subprojects download --sourcedir glib
 rm glib/subprojects/*.wrap
 mv glib/subprojects/ .
diff --git a/.gitlab-ci/run-check-todos.sh b/.gitlab-ci/run-check-todos.sh
index 8af102739..8a6a9bfda 100755
--- a/.gitlab-ci/run-check-todos.sh
+++ b/.gitlab-ci/run-check-todos.sh
@@ -2,11 +2,17 @@
 
 set -e
 
+ancestor_horizon=28  # days (4 weeks)
+
 # We need to add a new remote for the upstream target branch, since this script
 # could be running in a personal fork of the repository which has out of date
 # branches.
+#
+# Limit the fetch to a certain date horizon to limit the amount of data we get.
+# If the branch was forked from origin/master before this horizon, it should
+# probably be rebased.
 git remote add upstream https://gitlab.gnome.org/GNOME/glib.git
-git fetch upstream
+git fetch --shallow-since="$(date --date="${ancestor_horizon} days ago" +%Y-%m-%d)" upstream
 
 # Work out the newest common ancestor between the detached HEAD that this CI job
 # has checked out, and the upstream target branch (which will typically be
@@ -14,4 +20,11 @@ git fetch upstream
 # `${CI_MERGE_REQUEST_TARGET_BRANCH_NAME}` is only defined if we’re running in
 # a merge request pipeline; fall back to `${CI_DEFAULT_BRANCH}` otherwise.
 newest_common_ancestor_sha=$(diff --old-line-format='' --new-line-format='' <(git rev-list --first-parent "upstream/${CI_MERGE_REQUEST_TARGET_BRANCH_NAME:-${CI_DEFAULT_BRANCH}}") <(git rev-list --first-parent HEAD) | head -1)
+if [ -z "${newest_common_ancestor_sha}" ]; then
+    echo "Couldn’t find common ancestor with upstream master. This typically"
+    echo "happens if you branched from master a long time ago. Please update"
+    echo "your clone, rebase, and re-push your branch."
+    exit 1
+fi
+
 ./.gitlab-ci/check-todos.py "${newest_common_ancestor_sha}"
diff --git a/.gitlab-ci/run-style-check-diff.sh b/.gitlab-ci/run-style-check-diff.sh
index 1f7b8c125..b308e7679 100755
--- a/.gitlab-ci/run-style-check-diff.sh
+++ b/.gitlab-ci/run-style-check-diff.sh
@@ -2,21 +2,35 @@
 
 set -e
 
+ancestor_horizon=28  # days (4 weeks)
+
 # Wrap everything in a subshell so we can propagate the exit status.
 (
 
 # We need to add a new remote for the upstream target branch, since this script
 # could be running in a personal fork of the repository which has out of date
 # branches.
+#
+# Limit the fetch to a certain date horizon to limit the amount of data we get.
+# If the branch was forked from origin/master before this horizon, it should
+# probably be rebased.
 git remote add upstream https://gitlab.gnome.org/GNOME/glib.git
-git fetch upstream
+git fetch --shallow-since="$(date --date="${ancestor_horizon} days ago" +%Y-%m-%d)" upstream
 
 # Work out the newest common ancestor between the detached HEAD that this CI job
 # has checked out, and the upstream target branch (which will typically be
 # `upstream/master` or `upstream/glib-2-62`).
+#
 # `${CI_MERGE_REQUEST_TARGET_BRANCH_NAME}` is only defined if we’re running in
 # a merge request pipeline; fall back to `${CI_DEFAULT_BRANCH}` otherwise.
 newest_common_ancestor_sha=$(diff --old-line-format='' --new-line-format='' <(git rev-list --first-parent "upstream/${CI_MERGE_REQUEST_TARGET_BRANCH_NAME:-${CI_DEFAULT_BRANCH}}") <(git rev-list --first-parent HEAD) | head -1)
+if [ -z "${newest_common_ancestor_sha}" ]; then
+    echo "Couldn’t find common ancestor with upstream master. This typically"
+    echo "happens if you branched from master a long time ago. Please update"
+    echo "your clone, rebase, and re-push your branch."
+    exit 1
+fi
+
 git diff -U0 --no-color "${newest_common_ancestor_sha}" | ./clang-format-diff.py -binary "clang-format-7" -p1
 
 )
diff --git a/subprojects/gtk-doc.wrap b/subprojects/gtk-doc.wrap
index 7469d027b..79ec37220 100644
--- a/subprojects/gtk-doc.wrap
+++ b/subprojects/gtk-doc.wrap
@@ -2,3 +2,4 @@
 directory=gtk-doc
 url=https://gitlab.gnome.org/GNOME/gtk-doc.git
 revision=master
+depth=1
diff --git a/subprojects/libffi.wrap b/subprojects/libffi.wrap
index 6dea9ebed..00b29d6a2 100644
--- a/subprojects/libffi.wrap
+++ b/subprojects/libffi.wrap
@@ -2,3 +2,4 @@
 directory=libffi
 url=https://gitlab.freedesktop.org/gstreamer/meson-ports/libffi.git
 revision=meson
+depth=1
diff --git a/subprojects/proxy-libintl.wrap b/subprojects/proxy-libintl.wrap
index b53c8f7c3..6225021b8 100644
--- a/subprojects/proxy-libintl.wrap
+++ b/subprojects/proxy-libintl.wrap
@@ -2,3 +2,4 @@
 directory=proxy-libintl
 url=https://github.com/frida/proxy-libintl.git
 revision=0.1
+depth=1
diff --git a/subprojects/sysprof.wrap b/subprojects/sysprof.wrap
index 14874880e..fb669463b 100644
--- a/subprojects/sysprof.wrap
+++ b/subprojects/sysprof.wrap
@@ -2,3 +2,4 @@
 directory=sysprof
 url=https://gitlab.gnome.org/GNOME/sysprof.git
 revision=6b1cd7a722fcebae1ac392562c47957477ade8bf
+depth=1