This paper quantifies the nucleation energy barrier that must be overcome if a faceted, defect-free particle with a nonequilibrium morphology is to change shape by intraparticle transport. Two types of crystals are considered: those whose equilibrium form is a truncated sphere and those whose equilibrium form is a cube. Numerical estimates show that, for a particle near equilibrium, the barrier becomes insurmountable for a facet larger than a few tens of nanometers. For nonequilibrium shapes where material must be transferred from faceted surfaces to uniformly curved surfaces to reach the equilibrium shape, the facets enlarge without a nucleation barrier (at a rate limited by diffusion or surface attachment kinetics) until they reach a fraction of their equilibrium size that is typically between 0.5 and 0.75. At this point, a significant barrier is encountered that, in the absence of step producing defects, prevents the particle from continuing toward equilibrium. For nonequilibrium shapes where material must be transferred to faceted surfaces from other parts of the crystal for it to reach the equilibrium shape, significant energy barriers for the nucleation of new layers persist even when the shape is far from equilibrium. Predictions from our model are compared to experimental observations reported by other researchers.