No, you don't get double frequent flyer miles. As I recall, this issue was extensively discussed when Southwest first initiated this - a year or two back? - although I don't know where the thread is at this moment. I am pretty sure that this thread will be moved to TravelBuzz however.

edited to add ... I did a quick search on TravelBuzz and came up with this

http://www.flyertalk.com/travel/fttr...ML/007196.html

though it's not the thread I remembered, it may be a start.

[This message has been edited by CozumelJen (edited Mar 24, 2004).]