It is well known that in a well-defined load-controlled boundary-value problem for an elastic/perfectly-plastic structure the displacements are unique if the structure is everywhere elastic, and they are not unique at the yield-point load when the structure becomes a mechanism. The present paper is concerned with the range of contained plastic deformation between these two extremes. Several examples are given in which more than one displacement field exists for loads less than the yield-point load. The significance of this phenomenon is commented on from a physical, mathematical, and computational point of view.