How does one fish a steep, weedy dropoff from shore?

[MichaelAngelo]

Here's a challenging question for the best shore-fishing minds out there.

There's a lake I know that has quite a unique depth profile. It drops to 50 feet of depth just 20 or 30 feet out from shore. Making things more interesting is that there is a ring of tall weeds that extends for the first 10 feet out. My line is ploughing through the weedbed on each and every retrieve, killing sensitivity. If I was on the other side of the weeds, it wouldn't be a problem.

Any suggestions?