ulimit -n vs client_limit vs process_limit

As many of my users are accessing their mail remotely, I've seen service loads increase and came across this log messages which I haven't seen before

imap-login: Error: socketpair() failed: Too many open files: user=<*>, ...

I gather I have to increase file descriptor limits, which is currently set to match

default_client_limit = 1000

What should I set "ulimit -n" relative to client_limit? Or perhaps I've roofed

service imap-login {
	process_limit = 2
	...
}

and should adjust that?

Joseph Tam jtam.home@gmail.com