Can female dog be spayed while in heat or how soon after?

We've found a dog and no one claimed her. She was and still is in heat. We're trying to look for a home for her instead of taking her to a shelter. My vet suggests doing the spaying 4 weeks after she stops bleeding and my concern is what if she's pregnant already? We have no idea if she came into contact with a male dog before we found her and since we're looking for a home for her I have to be upfront about this and it's a turn off for possible new owners...

Yes you can fix her in heat, but it will cost more. You can also fix her if she is pregnant, but again- it will cost more.

She can be spayed if she is pregnant. She can be spayed if she is in heat. Both operations are more risky than a normal spay, done during the time between her seasons. Some shelters will even spay a puppy 8 weeks old, for heaven's sake! It's a simple operation, and most vets do so many that they can practically do them blindfolded.I had my collie mix spayed the first day she showed blood; it was her 6-month birthday. We were expecting a friend's dog the next day-- I had agreed to dog-sit while they went on vacation. He was an intact male Malemute mix twice her size; and I had NO intention of watching them play sex games for two weeks and then raising a litter of mutt puppies. She was utterly fine the next day.Discuss the possibilities with your vet; you might want a second opinion.