Although you cannot really see it here, I like to start my greyhounds sitting on a hill. It is not always necessary, but it can speed the process if you place your greyhound's rear end on the high side of a steep hill and point his nose down the hill. It makes it very easy for them to rock back and sit.
I like to use an easy to nibble treat like string cheese or a hot dog. Something the greyhound can take little bites of as I hold the treat over his head forcing him to crane his neck back.
I give the greyhound little bites of the treat I am holding as long as he continues to put forth the effort to target the treat, for rocking back, and for flexing the joints in the hind legs.
And then BAM! He sits! I continue to reward my greyhound for continuing to sit for a few seconds. Gradually I increase the length of time.
We have already talked about greyhounds having trouble with sitting and melting into a down. Be alert for the slightest sign that your greyhound is about to lie down. Step into him to prevent that from happening. I would much prefer my greyhound stand up than to lie down from a sit.
