Abstract A model of concentric, circular disc-shaped holes is used to describe the ledge-wise evaporation of low index crystal surfaces. Within the assumptions of the model, an exact solution is obtained to the problem of repeated nucleation of such discs on preferred surface sites. The model also provides an approximate solution to the transient development of the spiral shape, a problem heretofore unsolved. The results are compared with earlier theories of spiral evaporation. Required conditions are proposed for observing low values of the evaporation coefficient.