2³ bandaged

Two pairs of fused corners

Jaap Scherphuis: Bandaged 2×2×2

Numbers and Statistics
84 distinct positions
HTM: Solvable in 10 moves (5.42 on average)
QTM: Solvable in 15 moves (7.81 on average)

One pair of fused corners

Freshcuber: 2x2x2-Cube, Bandaged 1x1x2 (zwei Steine verklebt)

Numbers and Statistics
29,160 distinct positions. Of these (assuming WCA-4b3b would apply) 78 positions are not feasible for competition.
HTM: Solvable in 14 moves (9.79 on average)
QTM: Solvable in 17 moves (12.00 on average)