The good news: Peter aced his step test. He's quite willing to go up and down steps with no balking. Even better, he takes steps at a sensible speed and steps onto each step. Some dogs who are uncomfortable on steps will take a flying leap at the end of the staircase to eliminate those last few steps. Peter neatly took all the steps, even on short staircases where he could have jumped.
But, being Peter, every silver lining has its cloud. ;) I took him for a walk at the park and was letting him sniff at leaves and sticks and rocks and whatever else he was interested in. He ate something hard--didn't sound like either stick or rock, so I don't know if he found a piece of hard candy or a bit of bone or what. ETA: I've discovered he's fond of acorns. --KF 9/20/13
I haven't been muzzling him on walks at home because people here are pretty good about not throwing out things that would be hazardous to wildlife (or wild dogs). But I muzzled him for the rest of our walk at the park so he could sniff to his nose's content without finding anything else to eat.
Muzzled or not muzzled, he's not attracting a lot of people who want to pet him. It may just be that we were running into people who've never met a greyhound. Peter is a tall dog, and maybe people are intimidated by his size and his stripes. But at least I kept him from jumping people at the library (where we practiced short steps) and at the park.