Painting white is very difficult. I've recently been painting figures in an off white gray, dry brushing the figures in raised areas with white and then finishing with titanium white oil paint in the highest places.
Thats pretty much what I do. Base coat of pale grey, then white (but not dry brushing for the big figures. I'd dry brush with 15mm). A final highlighting with the purest white available. This includes re-painting the straps.But on a green wargames table, troops in white stand out the most so the hard work is worth it.