How to achieve a rolling update with docker-compose?

I have a following setup in docker compose

nginx for proxying to frontend, backend and serving static content
backend app on port 8080 (spring boot)
frontend app on port 4000 (node for SSR)
mysql used by backend

Frontend can be updated relatively fast using

docker-compose up -d --no-deps frontend

Unfortunately backend takes about 1 minute to start.

Is there an easy way to achieve lower downtime without having to change the current setup too much? I like how simple it is right now.

I would imagine something like this:

Start a new instance of backend
Wait till it starts (it could be per timer or a healthtest)
Close the previously running instance

Solution

Here is the script I've ended up using:

PREVIOUS_CONTAINER=$(docker ps --format "table {{.ID}}  {{.Names}}  {{.CreatedAt}}" | grep backend | awk -F  "  " '{print $1}')
docker-compose up -d --no-deps --scale backend=2 --no-recreate backend
sleep 100
docker kill -s SIGTERM $PREVIOUS_CONTAINER
sleep 1
docker rm -f $PREVIOUS_CONTAINER
docker-compose up -d --no-deps --scale backend=1 --no-recreate backend
docker-compose stop http-nginx
docker-compose up -d --no-deps --build http-nginx