Asymmetry in the wings and tails of birds is an unusual trait in that, because of their aerodynamic function, the optimum phenotype for the trait is known: perfect symmetry. There is considerable variation from this optimum both within and between species. Here I use simple aerodynamic theory to predict the aerodynamic costs of asymmetry in the wings and tail, and to examine the relation between the length of the wings or tail, and the cost of given amounts of absolute asymmetry (equal to a given fixed length) and relative asymmetry (asymmetry equal to a given proportion of the length of the wings or tail). The aerodynamic analysis shows that wing asymmetry is much more costly than tail asymmetry, and asymmetry in the aerodynamically functional parts of the tail is more costly than asymmetry in ornaments such as tail streamers. The cost of wing asymmetry and of asymmetry in aerodynamically functional parts of the tail is unaffected or decreases with trait length. In contrast, the aerodynamic cost of asymmetry in tail ornaments increases with trait size. Much of the pattern of variation in the level of fluctuating asymmetry in the wings and tail can thus be explained by natural selection for aerodynamic efficiency.