I see this all the time at the dog club. There are many breeds with particularly delicate throats and dogs that have had throat problems (genetic as well as from bone and toy related injuries).
You should purchase an Italian Greyhound collar (or whippet collar if she gets a bit bigger). These are specially designed martingale type collars for delicate necks. Below is a picture of the line I carry for the Club shop to give you an idea of what they look like. The part that sits over the trachea is wider and the ones I prefer have the collar and the (wider) neck-support seperate so when the collar pulls the neck-support doesn't. Anyway - do a search on Italian Greyhound collar and I'm sure you'll find something similar over there.
Interesting design. What brand? Couldn't really see the logo. I'd like to check for something like that around here. Olive's good with the Lupine but who knows - a girl can never have too many accessories.

