The pelvis of Pungitius pungitius (ninespine stickleback) is normally a robust, bilaterally symmetrical structure with stout spines. In some populations it is reduced in size, sometimes to complete absence. The first sign of reduction is loss of the spines, which is accompanied by a reduction in the size of the pelvic bones (vestiges) and an increase in bilateral asymmetry. Further reduction in the size of the vestiges leads to their eventual loss. In a pelvis-reduced population the propensity to spine asymmetry is highly heritable (h2 = 0.8 5 +/- 0.14) but asymmetry of the bony vestiges in fish without spines is not heritable. The absence of spines is heritable, as is size of the bony vestiges (h2 = 0.49 +/- 0.12). Crosses of spineless fish from a reduced population with spined fish from either of two normal populations produce only spined progeny. The inter-population heritability of pelvis size is h2 = 0.26 +/- 0.10, but that of bilateral asymmetry is zero. The expression of spines and vestiges is influenced relatively little by variation in pH, calcium, and salinity. We propose a polygenic model of inheritance with two phenotypic thresholds, the upper for the presence of spines and the lower for complete absence of the pelvis. Canalization breaks down between the thresholds. This genetic system probably predates divergence of the stickleback genera. We discuss its relevance to understanding the dynamics of pelvis reduction in extant and fossil stickleback populations.