Realistic predictions for the arrival directions of ultra-high-energy cosmic rays require extensive simulations of UHECR propagation through 3D space, potentially even including cosmological evolution and timing effects. Such 3D or 4D simulations of cosmic-ray propagation suffer from the fact that a relatively small target -- the observer sphere -- needs to be hit. If particles are ejected in any direction from the source according to the source emission geometry, such simulations are tremendously inefficient. We present here a targeting mechanism which finds an optimal emission geometry to maximize the number of hits while remaining unbiased in the arrival-direction distribution. This can lead to speedups by many of orders of magnitude, depending on the simulation setup. We present the basic mathematics to produce unbiased results from targeted simulations, demonstrate its effectiveness with the simulation package CRPropa 3 for various propagation scenarios, and discuss prospects to include this mechanism as a standard part of CRPropa in the future.