Thanks for the tips, people.
They have been very helpful.

My experience has taught me to set app mem to 2.5 times the prefered size. I've had good luck running at 12MB, so I'm going to try the 2.5x rule ... setting it to 5.5MB ... and letting Java do whatever .........

I'm not sure if setting the memory size down or setting connections to 2 did the trick, but now I'm getting connected to hundreds of other hosts instead of a couple dozen.

However, I'm finding LW is *EXTREMEMLY* sensitive to system loads. It flails around and dies if I have my MP3 player running at the same time. So I've had to shut the tunes off to download more tunes. Also just being in the connection window while LW is trying to connect causes it to flail around and not get connected. If I go back to the search window, *BANG* .... I get connected quick to piles of hosts. Finally, just doing two downloads over my 56K link [running around 50K] is enough to cause my connections to go down. I'm at the point where I disconnect once I get two or three downloads going, and then reconnect when I'm ready for more downloads.