BTW - if Gene is comfortable in a sheet like that, it might be a good opportunity to try to get Gene used to you towelling him/her. There are lots of ways to approach it. One way is to use a towel when playing with him/her and gradually try to put it around Gene's body.
Oooo sorry, I didn't explain myself. By toweling I mean, being happy to be restrained in a towel - the towel is around the bird and your hand is around the towel on the bird's back. I hope that makes sense. It's a really useful behavior to train for if you want to file/trim your bird's nails or take him to the vet for a checkup. If the bird isn't comfortable being restrained by a towel, the vet visit can be very stressful for the bird (and you). I should also add mine AREN'T towel trained. I've tried unsuccessfully in the past. Starting young is a good idea.