Nginx 1.10.3: Alternative to upstream server max_conns

I've got a server running open source Nginx 1.10.3 with a pretty simple config: Serving static files, in case a file doesn't exist, the request is send to a backend.

I need to limit the active connections to this backend. Quite easy, isn't it, using upstream server max_conns, which

limits the maximum number of simultaneous active connections to the proxied server.

Besides, this was only introduced in 1.11.5, so it's not (yet) available for me.

Any clever ideas / workarounds out there dealing with this situation?

[This server is currently running Debian jessie with nginx out of jessie-backports. I could upgrade to stretch, and use stretch-backports. But, before doing so, and because I'm quite happy with this system, I would like to check if there is any other way around. You know: Never change a running system...]