How to give a short speech

I often get asked about short speeches, and off-the-cuff remarks.  How do you do them well?  What are the pitfalls to avoid?  It can be surprisingly hard to say something interesting in a very short time, and to avoid running on at the mouth and saying too much.  What's the happy medium, and how do you think about it?

First, I would distinguish between responding to a question, or making a statement of less than a minute or two, and making a short speech of, say, 5 to 7 minutes.  Time constraints necessarily make them two different genres.

The minute speech is best handled as follows.  Decide what you're going to say, take a deep breath, and then give the headline.  "I don't think that mice should be allowed in the Vatican."  Then go on to give up to 3 supporting reasons, depending on your thinking and the time allowed.  Hygiene, worry about the destruction of precious manuscripts, and the eek factor during prayers.  Finally, finish off with a repetition of the headline:  "So that's why I think that mice should be banned from the Vatican."

When you've got more than 3 but less than 7 minutes, think in terms of problem-solution.  If you have a great story to begin the problem section, then do so, but don't allow it to take over the problem section entirely.  You need to spend half of your allotted time discussing the problem in as much detail as you can (which is not much).  Heretical mice are running amok throughout the Vatican.  This deplorable plague has led to illness, destruction of some of the Vatican's most precious artifacts, and the discomfort of many visitors and residents....About half way through your total time, switch to the solution and buttress that with as much logic and passion as you can muster.  I recommend beginning with an excommunication, followed by mice traps, poison, and the playing of Barry Manilow recordings in the basement.... 

That's really all there is to it.  Keep it simple.  If you want to conclude by describing the benefits of your solution, then go ahead, in a sentence or two. 

Repetition and simplicity will help you keep your remarks organized and under control, and will help your listeners follow you.