While on my ENT months I did a lot of quick reviews on topics (e.g. you're seeing a consult, etc) with Pasha's, focused reading in Bailey's, review articles (sometimes at attending direction), etc. A lot like a sub-i, but more in-depth. Try to read about anything that isn't familiar.
Once I left my otolaryngology months, I tried to do a systematic reading schedule. A chief when I was a med student once told me my goal should be between 5-7 hours of reading per week (or about 45 minutes to an hour per day outside the hospital). He said it didn't matter that you did it every day, just try to hit your goals and make it a habit. I think that was great advice and a reasonable goal, though I do admit there are some months I slacked off and focused more on mindless stuff when I got home (December was a long cold month on a busy gen surg service where I barely touched anything). I've tried to get through Bailey's this way and have made a pretty good dent in it. Also read some articles in Laryngoscope and Oto-HNS along the way.
But intern year is intern year, even with the new hour restrictions you'll have your times you're burnt out. You shouldn't feel pressured to read during those times, it'll only make things worse. The main thing is to make it a habit and try to cover a little of everything (Bailey's was helpful that way, and is easier to read than Cummings IMHO).
Caveat: Just finishing intern year, have no idea is this is a "good" strategy or not.