I'm a Tele player, and I learned the trick from Danny Gatton's Hot Licks instructional tape, where he showed how to cut away some of the attack with volume swells, and also tone swells. He did this on a Tele with standard control plate setup. Simply, you wrap your pinky around the volume knob.
(Jeff Beck uses a tone swell for the train horn lick at the intro to the Yardbirds' "Train Kept A' Rollin'".)
I went to a reversed control plate (volume, tone, switch instead of switch, volume, tone) so I can reach these knobs more easily. I still do that, but lately, I've taken to using a Morley volume pedal to do this, so I have fewer things going on with my hands.