I've gotten good results at 3200 and 6400 with the 60D if I over-expose a stop or two. Or as they say around here, ETTR (expose to the right, on the histogram). Would be a good time to shoot RAW instead of jpeg too, if you aren't already. You might try this with your T3 for that matter and see if there's an improvement.
Also helps if you don't pixel peep at 200%.
Agree with this. i've gotten usable results up to 6400 if i ETTR. And yes, always shoot RAW. I had a T3i a when they first came out and contrary to what some may say, the 60D is way ahead. Same sensor...yes. But, pentaprism vs pentamirror...yeah...60D win. 2 dials, 1 for aperture and 1 for SS...win again. Top LCD (nostalgic for us film shooters)...Win.
Etc...Etc...i think you get the picture