I had very low HDL. I was able to raise it to a healthy level by going from not drinking any alcohol, to drinking half a glass of wine at dinner every night, and from almost no animal fats, to two egg yolks a day (along with the whites of course).
I was exercising daily and this did not change it. My LDLs were never a problem, but DH's were, hence the no animal fat diet.
YMMV.
Doctors are reluctant to suggest alcohol because the potential risks of alcoholism are so high, and someone can be a latent alcoholic and not know it. I watch myself like a hawk, and so far I do not crave any more alcohol. Of course I'm too frugal to buy really good wine, so that may help.