All posts on here have great advice and I agree with it all 100%! Also, I am a great advocate of having a "proper" warm-up and "warming down", as well. One of my private teachers taught me that a good warm-up should consist of long tones, some nice slurring, on the lower and middle registers and some short staccato passages, to get your tongue working. Then you can add a few regular scales and some chromatic scales. All this should encompass about 15 min worth. This has always worked great for me! I feel it really primes your chops and gets you ready to go!
I also feel that a good "warm-down" is very important; especially after you've been playing for a long time or have just gotton done playing a number of very strenuous/demanding pieces of music, and your chops are very "tight". For me, a warm-down consists of some good, long tones, starting on low C and then continuing down chromatically to "peddle tones". We used to do a lot of warm downs, with both long tones on the lower register and peddle tones, when I was in Crossmen, especially in 1990, and it always helped us immensely. It's a great way to loosen up and you'll also find that, in a lot of cases, your chops are less tight the next day, when you go to play.
In my opinion, "warm-downs" are especially good for high brass players, who have been doing a lot of heavy playing in the upper register, for long periods of time.
P.S. - Bill, great idea about the "pencils"! Brings back memories for me, as we had a thing we used to do in the lead sop line in Crossmen 1990: We would take our mouthpieces out and turn them upside down, bow our heads, then put the shank of the mouthpiece between our lips and hold it there as long as we could!