evenflow, I know what you mean.
I was doing 27L departures last month, very busy, 15-20 at the hold. Just had an emergency land on 27R, closing the runway for 10 mins, so we had a few landers on 27L, this was followed by TEAM with continuous landings on the departure runway because inbound delay had reached 40 minutes. However, the gaps were only 8 miles so not really allowing me to get a decent flow going. I had a Cat B helicopter operating nearby so traffic info had to be passed to everyone.
I had three a/c call me for their sequence number in one minute, and to the last one I said: "I'll call you back when I can, I'm very busy."
Another minutes passes and "Uuuh, tower, request our number for departure."
"Okay, the next one to ask for their sequence will be last"
Peace and quiet!
Gonzo.