The body axis of vertebrate embryos is periodically segmented into bilaterally symmetric pairs of somites. The anteroposterior length and boundary position of somites are thought to be molecularly determined prior to somite morphogenesis. We show that in zebrafish embryos, initial somite lengths and positions are imprecise and many somites form left-right asymmetrically. Yet, within an hour, lengths are adjusted, becoming more symmetric, through somite deformations occurring independently on the left and right sides of the embryo. This adjustment is directed by a combination of somite surface tension, external stresses from neighbouring tissues and convergence-extension flows within somites. The ensuing left-right symmetry in somite boundary positions follows as a straightforward consequence of the length adjustments. Thus, the precision and symmetry of a fundamental embryonic morphological pattern is ensured by tissue mechanics.