This is what I kept forgetting, as most puzzles of these sorts don't need them.

However, many puzzles in Tametsi need this.

If you have are at a point where it seems there are no further moves, remember each puzzle requires a single unique solution.

If you have a choice of three possible cells to eliminate, check that if you eliminate one, that it DOESN'T make the other two options BOTH valid. This would mean the puzzle has two solutions.

Therefore, the cell you first chose CAN'T be eliminated, as it would break the rule of each puzzle having a single solution.

You have no idea how often this was what was keeping me from seeing the next move...