Mary Kuhner wrote:
We don't teach kotagaeshi, but a similar throw, koteoroshi, which is more straight up and down (it's thought to be safer for the wrist, I believe)....Mary Kaye
Kote-oroshi was developed from kote-gaeshi. Kote-gaeshi was eliminated from the Ki Society curriculum since it was discovered students were concentrating on the wrist turning motion. There are people who have either strong wrists that you can't turn or others who have extremely flexible wrists who you can turn all the way over.
In both kote-oroshi and kote-gaeshi the important thing is to lead the uke around and then down. If you lead from the fingers then you turn them down before throwing (kote-gaeshi - wrist turning). If you lead from the wrist, you can just drop it (kote-oroshi - wrist drop) at the end of the technique. To my simple way of thinking a kote-oroshi is just a kote-gaeshi done right.
In the Ki Society kote-oroshi is practiced without atemi. However, atemi can be used in both kote-oroshi/kote-gaeshi.