Didn't really want to jump into this fray <G>, but for someone to say that saying expedite is poor phraseology is in a British term "rubbish"
Some places it is perfectly good phraseology and you will use it to convey to the pilot community that you do not want them to delay their climb or descent. You want them to smartly move the aircraft. This may or may not mean a particular rate of climb or descent, but may also mean that when the aircraft is climbing out we don't want you to use econ climb nor do we want you flattening out your climb to pick up speed. We want you to expedite your climb or descent through a particular altitude. That is not real ambiguous in and of itself.
Now, that said, I will also not "assume" that this phrase alone will guarantee separation. I do that with a crossing restriction, however, I may not need a crossing resrtiction for quite a while and to just get them up or down and out of the way quickly will indeed suit my needs. I will monitor the situation and it is not working, then I will come up with plan B or even C. For whoever mentioned that I don't know the fuel load or the weight and other issues, you are correct. But I do have a very good idea of what the aircraft can or can't do by what sort of aircraft it is, who it is flying for and where it is going. What I can't take into account is who is flying it. Everyone flys thier aircraft differently, and if you want to try to get someone to speed things along a bit in a climb or decsent, then that is what the word expedite is for. Let the pilot know what your expectations are, I need you to not dawdle, get that thing moving in the direction that it is headed. If not, then you can expect to do something else... Remember in a constantly changing environment with traffic not always under your own control, you have to grab for all the tools in your bag, and this is but one of them...
regards
Scott