A computer simulation of the Er3+ 3-μm crystal laser considering the full rate-equation scheme up to the 4F7/2 level has been performed. The influence of the important system parameters on lasing and the interaction of these parameters has been clarified with multiple-parameter variations. Stimulated emission is fed mainly by up-conversion from the lower laser level and in many cases is reduced by the quenching of the lifetime of this level. However, also without up-conversion a set of parameters can be found that allows lasing. Up-conversion from the upper laser level is detrimental to stimulated emission but may be compensated by cross relaxation from the 4S3/2 level. For a typical experimental situation we started with the parameters of Er3+:LiYF4. In addition, the host materials Y3Al5O12 (YAG), YAlO3, Y3Sc2Al3O12 (YSGG), and BaY2F8, as well as the possibilities of codoping, are discussed. In view of the consideration of all excited levels up to 4F7/2, all lifetimes and branching ratios, ground-state depletion, excited-state absorption, three up-conversion processes as well as their inverse processes, stimulated emission, and a realistic resonator design, this is, to our knowledge, the most detailed investigation of the Er3+ 3-μm crystal laser performed so far.