I know this is an old thread, relatively speaking since R2R is pretty on top of things, but I've found that a combo works. Getting rid of nitrates and phosphates is always a good option, but there are times that you still get bryopsis or hair algae, something. What works for me is peroxide and forced tank rehab. There is something wrong if I have hair algae growing on my rocks and in my tank, so I take it out, peroxide the parts of the rock that are infected, scrub the rest, vaccum my sand bed super well, drain most of the water out of the tank, get a cloth with peroxide and scrub the glass clean, toothbrush the corals around them so I don't directly peroxide them (although I've never had an issue with dipping corals in 3% H2O2 mixed 50/50 with old tank water, SPS, LPS, softies, zoas, shrooms, etc.), basically just get the problem out with some work, and it doesn't come back. Well, until I do something stupid like introduce a cool frag from a friend or something.

Point is that with some work, you can get rid of it and fix the problem causing it at the same time (reduce feeding, lighting, add GFO or Phosguard for quick removal, etc.). Basically just make the tank behave like I want it to, and then fix the stupid thing I did to cause it in the first place. Just like brushing my teeth and flossing. Same concept. I don't believe in putting something in the tank and then waiting for something good to happen. That's like telling me to just keep eating an apple a day and that'll keep the doctor away... Not my style. Just make it happen the way you want it to happen and don't let the algae stick around any longer than you want it to.
Just my $0.02....