I recently saw some old footage of Joni Mitchell playing her wonderful song 'A Case of You' back in the 70s (from the 'Blue' album). She was playing her guitar flat on her lap. I downloaded the guitar tab and tried playing the chords normal style and then with the guitar flat on my lap. The latter sounded much better. The vibrato you can achieve playing 'flat' is much stronger, I found, and the strings can be 'snapped' to good effect too.

Does anyone know of other musicians who have played particular songs with the guitar played flat on their laps? Does it add to the sound in your opinion?