"refreezing" F/T mice

[Jim Smith]

There have been occasions where I've thawed out a couple of mice for one of my snakes and they are not in the mood to eat. Usually, I am able to offer them to my larger female Honduran who can be a bit of a garbage disposal, but since she's eating larger mice, she's usually full up. My question is do any of you re-freeze the mice to thaw out and feed at a later date? When this has happened in the past, I toss the uneaten mice out, but I was just wondering if this is necessary.