Remember that when you fly on a paid flight, even if it is paid by a voucher you earned by volunteering to be bumped, you have a choice of partner airlines miles programs in which you can put your miles. For example, British Airways allows you to put flight miles into American or Alaska Airlines programs, last I looked. So chose the airline in which you want to earn miles, and funnel all of them there.

U.S. airlines often charge considerably less in "fees" on your award ticket than do those in Europe. Also, U.S. airline tend to have many more ways of earning mega miles without actually flying - see my website below.

American Airlines is particularly good at being able to acutally give you an award ticket when and where you want to travel.