Suppose your unmasking piece is one move away from giving check or inflicting some other terrible threat; the problem is that the masked piece has nothing suitable to attack. Perhaps the target at the other end of the file is protected, or not very valuable. Again, there are some standard ways to try to draw a good target into the path of the discovery.
In the diagrammed position here, White has the kernel of a discovered attack on the d-file. The bishop has a good threat to make: Bxg7 gives check. But the rook behind it lacks a good target once it is unmasked. It can take the knight on d7 (and avoid being recaptured because it would have cover from the bishop on b5); but meanwhile the White bishop would have been sacrificed, so the net gain for White would only be the pawn on g7. The discovery would work better, and would indeed look like many good discoveries we have seen, if a more valuable piece—i.e., Black’s queen—could be made the target of the unmasked rook. The method for arranging this is simple: when you are confronted with an unsuitable target like the d7 knight here, ask whether you can first take it with another piece and what the consequences would be. Here White can capture with BxN; Black’s only recapture is QxB. If Black goes through with that move, the exchange has caused the bad target to be replaced with a good one. Now Bxg7+ unmasks a classic discovered attack against Black’s queen, which is lost after Black fends off the check.