Magnetization reversal in a perfect ferromagnetic prolate spheroid, wi
th no surface anisotropy, is known to start from nucleation either by
coherent rotation (for small radii), or by the magnetization curling m
ode (above a certain size), but the possibility of a third mode has ne
ver been ruled out. It is rigorously proved here that there can be no
third switching mode if the aspect ratio is not larger than 500:1, and
even for larger ratios it may at most exist for a very limited size r
ange.