I purchased this sports bra to wear during my martial arts classes, so I was specifically looking for ones I thought would compress my larger chest well.  I know this isn't what every woman is looking for, so keep that in mind.
I did a light work out today as a trial run, and the bra stayed in place well.  I didn't notice my breasts falling out of the bra, nor did I have to constantly readjust.  This bodes well for harder workouts.
However, the elastic band that goes around the chest is just naked elastic.  It's not covered by anything, so it's uncomfortable.  I'm sure that during a heavier workout when I'm sweating a lot and moving more, it'd chafe.  So I'll wear a light tank top or something underneath--and that's fine--but not really different than my previous strategy of wearing two medium-support sports bras at once.  That was something I was trying to avoid.  If I don't like that, I'll still keep these bras (I bought one in black as well) for lighter workouts and cross-training instead of the dojo.