The deal is, after identifying and clearing the complete lines, identify all independent block clumps above the first cleared line, and then have them drop independently. Preferably, drop all blocks between first and second line, if any, and then the next level and so on. In round robin fashion, drop each clump by one square.

Also will have to look for any new lines and repeat.

*http://gamedevelopment.tutsplus.com/tutorials/implementing-tetris-clearing-lines--gamedev-1197

"Move" them instead of blitting in and out their positions.