-SAT allows three literals per clause: "a OR b OR c." This is NP-complete. No known fast algorithm exists. The jump adding one more variable per clause changes everything.
If you have constraints with more than two options, you might need backtracking, branch-and-bound, or approximation algorithms. -SAT is the right balance: expressive enough for many problems, simple enough to solve in linear time. It is a rare case where a restriction makes a hard problem tractable.