  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.
