I posted this elsewhere, but I really think this is the problem with the team. Rondo spoke out in the media about someone griping in the locker room about not getting enough touches and playing for a contract.
A few games later, Perk complained in the orlando game about not getting enough touches and was benched for the rest of the game (the game was tight and we could have used him against superman) but he was being punished. Doc made him sit in the "time out" chair.
Doc needs to find a way to assimilate Perk into this team. There aren't that many shots for him with the first unit. But he is a good high percentage shooter and Perk has a good point that he should get more touches. His defense is also extraordinary.
So, I think Doc should make Perk the sixth man off the bench with the second team. (Let Sheed start.) Perk could become a go to guy for the second unit. He may even shoot an even higher percentage against the other teams second string as well. I would rather see him taking shots in the paint than seeing BBD on the second team having his lunch handed to him any time he tries to shoot in the paint.
Sheed and Baby aren't a good combination on the floor - but we saw last year that Perk and Baby made a good combination on the floor. This move is a no-brainer. The second team is good, this will make them better.
Doc - don't be so stubborn and give this a try. Though it may seem like a demotion from first string to second string, if you made Perk a go to guy for the second unit, it may not be perceived as a demotion. Think about it. You have to do something and this might also solve your locker room problems, second team performance issues, etc ...