The squeezed states of a spin-1/2 particle are described, and the response of such a particle to sudden illumination by a resonant, circularly polarized, coherent electromagnetic wave in the absence of relaxation is given. It is shown that the resultant undamped Torrey nutations (Rabi flops) lead to periodic squeezing of the spin states. The error ellipsoids associated with the minimum-uncertainty states for this system are presented. The implications of these results for the squeezing of the field vectors of the electromagnetic radiation emitted by spins and quasi-two-level atomic systems (in states which have been prepared by coherent transient driving fields) are pointed out.