Theory predicts that genetic and phenotypic correlations among traits may direct the process of short-term evolution by limiting the directions of variation available to natural selection to act on. We studied correlations between 14 skeletal traits in 10 geographically distinct and relatively young greenfinch (Carduelis chloris) populations to unravel whether the divergence among populations has occurred into directions predicted by the within-population correlations (cf. drift/correlated responses models), or whether it is better explained by ‘adaptive’ models, which predict no necessary association between within- and among-population correlations (allometries). We found that the within-population character correlations (or covariances) did not predict character divergence between populations. This was because the first eigenvector of the among-population correlation/covariance matrix, summarizing the major dimension of divergence, was a bipolar body:beak dimension, and distinct from the (≈ isometric) first eigenvector of within-population matrix. Hence, as the divergence among greenfinch populations cannot be satisfactorily accommodated by drift/correlated response models, an adaptive basis for divergence is suggested. The second major axis of within-population variation was a classical ‘group size’ factor revealing that beak size was more or less free to vary independently of body size. Consequently, even if the divergence among populations cannot be simply accommodated to expectations of drift and correlated response models, it is striking that the most pronounced size-independent (nonallometric) changes had occurred along the second largest dimension of variance. This could mean that selection pressures which shape integration within populations are the same as those that cause divergence among populations. A relaxed beak:body integration could also occur as a result of species level selection favouring taxa in which independent evolution of beak and body is made possible.