I'm pretty cut throat when dealing with my DL/NA guys. I usually cut them unless they're complete studs.
On one team, I had to drop Andy LaRoche, Wily Mo Pena, and Colby Rasmus to clear space for BJ Ryan, Pedro Martinez, and Mike Cameron. They also just got back Josh Beckett. I put myself at a disadvantage by drafting a guy who I knew was heading for the DL when I got them (Ryan twice, Escobar, and Kazmir) though so I shouldn't really complain.