Mike,
I agree with Paul that the use of kotegaishi is dependent on the context of the environment and also of the intent and intensity of the attacker.
It's nice to have in the bag of tricks when you're in situation that requires "controlling" rather than striking/knocking down, such as a school, hospital, community center. Also, when the "opponent" is someone you really do not want to seriously hurt for whatever reason.
Frankly, though, against a determined opponent, I am not sure that a kotegaeshi without a "softening" prelude, i.e. atemi, can be counted on to take an opponent down. Folks with strong arms and wrists can fight off the grasp before the technique is affected. People with pliable wrist can actually take alot of pressure before damage is done (or be made to flip over to relieve the pressure.) In that interim, they can strike you back. Someone who knows how can also foil the kotegaeshi. Rather than resisting the pressure, stay loose and move into the proponent. This takes pressure off the wrist and gives you time to close and counterstrike and/or grab onto the person and pull him/her down with you. I've tried this in a fast randori with someone I trusted to not get mad at me because I broke from the role of "uke" to "nage" (or "tori"). I didn't tell him beforehand because that would nullify the idea of the test. But, essentially, when he got hold of my wrist on a tsuki attack and went for the kotegaeshi, I flowed in to him, grabbed him by the back of the neck and pulled him with me into the breakfall. The grab could easily been replaced with a strike to his temple or something else. Of course, if I hadn't moved fast enough, my wrist could have been strained or broken. But that would have been my fault and not his.

Anyway, I believe in atemi, atemi, atemi and maybe a kotegaeshi to follow with a strong/determined opponent. I would apply the same approach to other types of wrist manipulations like nikkyo and sankyo.
Mike, do you have tapes of your bunkai interpretations with jujutsu responses? That could help Lori and others better visualize/remember the techniques.
david
[This message has been edited by david (edited September 16, 2000).]