  We study the computational complexity of the Buttons \& Scissors game and
obtain sharp thresholds with respect to several parameters. Specifically we
show that the game is NP-complete for $C = 2$ colors but polytime solvable for
$C = 1$. Similarly the game is NP-complete if every color is used by at most $F
= 4$ buttons but polytime solvable for $F \leq 3$. We also consider
restrictions on the board size, cut directions, and cut sizes. Finally, we
introduce several natural two-player versions of the game and show that they
are PSPACE-complete.
