It's the first time I subbed 40 s without 1-key finesse. Though, I couldn't do it with 1 preview and completely random piece order. This video is a part of my *requirements of fast paced Tetris* studies.

http://harddrop.com/forums/index.php?showtopic=4343

Bag randomizer, 2 previews 38.45 s (2.60 pps)
Bag randomizer, 1 preview 41.81 s (2.44 pps)
Memoryless rand., 2 previews 40.73 s (2.50 pps)
Memoryless rand., 1 preview 41.83 s (2.39 pps)

From my experience the number of previews is a more decisive factor than the randomizer. With 2 previews, I could maintain a better flow, i.e. in average smaller pauses between dropping a piece and moving the next one. With completely random piece order, I had to stop more often, because I didn't see a good spot for the current piece fast enough.