With detailed measurements of flight-related morphological parameters of 18 species within the tribe Heliconiini and 10 of their non-heliconiine comimics, I found that morphological parameters relevant to flight biomechanics are associated with three escape tactics of these Neotropical butterflies: evasive flight, distastefulness, and mimicry. Two distinct character suites, one pertaining to the position of centre of body mass and another pertaining to wing shape, were identified using principal-components analysis. A third component correlated most highly with the position of centre of wing mass. Mimicry groups were best discriminated by the positions of centres of body and wing mass, suggesting that these features converged within mimicry groups. Centres of mass were positioned nearer to the wing base in mimicry groups composed of more palatable species, presumably decreasing the radial moments of inertia of the body and wings and increasing flight speed and turning performance. Predation has selected for body morphology that increases flight speed and manoeuvrability in palatable butterflies, whereas the morphology of distasteful species compromises flight performance. Convergent selection may reduce morphological differences of species within mimicry groups arising from distantly related lineages, and hence it may have enhanced the morphological diversification of palatable and unpalatable butterflies within lineages that have more recently evolved distastefulness.