diff --git a/changes/ticket32216 b/changes/ticket32216
new file mode 100644
index 0000000000..86712d700d
--- /dev/null
+++ b/changes/ticket32216
@@ -0,0 +1,9 @@
+  o Minor features (git scripts):
+    - Make git-push-all.sh skip unchanged branches when pushing to upstream.
+      The script already skipped unchanged test branches.
+      Closes ticket 32216.
+  o Minor bugfixes (git scripts):
+    - Avoid sleeping before the last push in git-push-all.sh.
+      Closes ticket 32216.
+    - Forward all unrecognised arguments in git-push-all.sh to git push.
+      Closes ticket 32216.
diff --git a/scripts/git/git-push-all.sh b/scripts/git/git-push-all.sh
index 7e67f4c96d..ebfa576196 100755
--- a/scripts/git/git-push-all.sh
+++ b/scripts/git/git-push-all.sh
@@ -29,6 +29,8 @@ function usage()
   echo "       CI environment failures, using code that previously passed CI."
   echo "       (default: skip; current: $CURRENT_PUSH_SAME matching branches)"
   echo "   --: pass further arguments to git push."
+  echo "       All unrecognised arguments are passed to git push, but complex"
+  echo "       arguments before -- may be mangled by getopt."
   echo "       (default: git push --atomic, current: $GIT_PUSH)"
   echo
   echo " env vars:"
@@ -127,9 +129,11 @@ while getopts ":hr:st:" opt; do
        OPTIND=$((OPTIND - 2))
        ;;
     *)
-       # Assume we're done with script arguments,
-       # and git push will handle the option
-       break
+       # Make git push handle the option
+       # This might mangle options with spaces, use -- for complex options
+       GIT_PUSH="$GIT_PUSH $1"
+       shift
+       OPTIND=$((OPTIND - 1))
        ;;
   esac
 done
@@ -229,20 +233,31 @@ fi
 # Entry point #
 ###############
 
-# Skip the test branches that are the same as the upstream branches
-if [ "$PUSH_SAME" -eq 0 ] && [ "$TEST_BRANCH_PREFIX" ]; then
+if [ "$TEST_BRANCH_PREFIX" ]; then
+  # Skip the test branches that are the same as the default or current
+  # upstream branches (they have already been tested)
+  UPSTREAM_SKIP_SAME_AS="$UPSTREAM_BRANCHES $DEFAULT_UPSTREAM_BRANCHES"
+else
+  # Skip the local maint-*, release-*, master branches that are the same as the
+  # current upstream branches, but ignore the default upstream
+  # (we want to update a non-default remote, even if it matches the default)
+  UPSTREAM_SKIP_SAME_AS="$UPSTREAM_BRANCHES"
+fi
+
+# Skip branches that match the relevant upstream(s)
+if [ "$PUSH_SAME" -eq 0 ]; then
   NEW_PUSH_BRANCHES=
   for b in $PUSH_BRANCHES; do
     PUSH_COMMIT=$(git rev-parse "$b")
     SKIP_UPSTREAM=
-    for u in $DEFAULT_UPSTREAM_BRANCHES $UPSTREAM_BRANCHES; do
+    for u in $UPSTREAM_SKIP_SAME_AS; do
       UPSTREAM_COMMIT=$(git rev-parse "$u")
       if [ "$PUSH_COMMIT" = "$UPSTREAM_COMMIT" ]; then
         SKIP_UPSTREAM="$u"
       fi
     done
     if [ "$SKIP_UPSTREAM" ]; then
-      printf "Skipping unchanged: %s remote: %s\n" \
+      printf "Skipping unchanged: %s matching remote: %s\n" \
         "$b" "$SKIP_UPSTREAM"
     else
       if [ "$NEW_PUSH_BRANCHES" ]; then
@@ -255,6 +270,12 @@ if [ "$PUSH_SAME" -eq 0 ] && [ "$TEST_BRANCH_PREFIX" ]; then
   PUSH_BRANCHES=${NEW_PUSH_BRANCHES}
 fi
 
+if [ ! "$PUSH_BRANCHES" ]; then
+  echo "No branches to push!"
+  # We expect the rest of the script to run without errors, even if there
+  # are no branches
+fi
+
 if [ "$PUSH_DELAY" -le 0 ]; then
   echo "Pushing $PUSH_BRANCHES"
   # We know that there are no spaces in any branch within $PUSH_BRANCHES, so
@@ -267,27 +288,42 @@ if [ "$PUSH_DELAY" -le 0 ]; then
 else
   # Push the branches in optimal CI order, with a delay between each push
   PUSH_BRANCHES=$(echo "$PUSH_BRANCHES" | tr " " "\n" | sort -V)
-  MASTER_BRANCH=$(echo "$PUSH_BRANCHES" | tr " " "\n" | grep master)
+  MASTER_BRANCH=$(echo "$PUSH_BRANCHES" | tr " " "\n" | grep master) \
+      || true # Skipped master branch
   if [ -z "$TEST_BRANCH_PREFIX" ]; then
-    MAINT_BRANCHES=$(echo "$PUSH_BRANCHES" | tr " " "\n" | grep maint)
+    MAINT_BRANCHES=$(echo "$PUSH_BRANCHES" | tr " " "\n" | grep maint) \
+        || true # Skipped all maint branches
     RELEASE_BRANCHES=$(echo "$PUSH_BRANCHES" | tr " " "\n" | grep release | \
-      tr "\n" " ")
-    printf "Pushing with %ss delays, so CI runs in this order:\n%s\n%s\n%s\n" \
-      "$PUSH_DELAY" "$MASTER_BRANCH" "$MAINT_BRANCHES" "$RELEASE_BRANCHES"
+      tr "\n" " ") || true # Skipped all release branches
   else
     # Actually test branches based on maint branches
-    MAINT_BRANCHES=$(echo "$PUSH_BRANCHES" | tr " " "\n" | grep -v master)
-    printf "Pushing with %ss delays, so CI runs in this order:\n%s\n%s\n" \
-      "$PUSH_DELAY" "$MASTER_BRANCH" "$MAINT_BRANCHES"
+    MAINT_BRANCHES=$(echo "$PUSH_BRANCHES" | tr " " "\n" | grep -v master) \
+        || true # Skipped all maint test branches
     # No release branches
     RELEASE_BRANCHES=
   fi
-  $GIT_PUSH "$@" "$UPSTREAM_REMOTE" "$MASTER_BRANCH"
-  sleep "$PUSH_DELAY"
+  if [ "$MASTER_BRANCH" ] || [ "$MAINT_BRANCHES" ] \
+      || [ "$RELEASE_BRANCHES" ]; then
+    printf "Pushing with %ss delays, so CI runs in this order:\n" "$PUSH_DELAY"
+    if [ "$MASTER_BRANCH" ]; then
+      printf "%s\n" "$MASTER_BRANCH"
+    fi
+    if [ "$MAINT_BRANCHES" ]; then
+      printf "%s\n" "$MAINT_BRANCHES"
+    fi
+    if [ "$RELEASE_BRANCHES" ]; then
+      printf "%s\n" "$RELEASE_BRANCHES"
+    fi
+  fi
   # shellcheck disable=SC2086
-  for b in $MAINT_BRANCHES; do
+  for b in $MASTER_BRANCH $MAINT_BRANCHES; do
     $GIT_PUSH "$@" "$UPSTREAM_REMOTE" "$b"
-    sleep "$PUSH_DELAY"
+    # If we are pushing more than one branch, delay.
+    # In the unlikely scenario where we are pushing maint without master,
+    # or maint without release, there may be an extra delay
+    if [ "$MAINT_BRANCHES" ] || [ "$RELEASE_BRANCHES" ]; then
+      sleep "$PUSH_DELAY"
+    fi
   done
   if [ "$RELEASE_BRANCHES" ]; then
     # shellcheck disable=SC2086