algae growth and plant density

I was wondering if increasing the amount of plants on my tank will cut down
on algae growth. If I keep everything else
constant, light hours, CO2, etc...?
I have this persistant hair algae problem that I'm keeping under control
with tank cleaners, otos primarly, but once
they clean off a leaf, theres more algae growning a day later. I used to
have a thriving tank w/o algae and the only think I can
think of different between then and now is the number of plants in my
tank...
any opinions?