  We discuss a special class of Beltrami coefficients whose associated
quasiconformal mapping is bilipschitz. These are of the form the characteristic
function of a planar bounded domain with smooth boundary of class C 1+epsilon
times a density of class Lip epsilon on the domain. The crucial fact in the
argument is the special extracancellation property of even Calderon-Zygmund
kernels, namely that they have zero integral on half the unit ball. This
property is expressed in a particularly suggestive way and is shown to have
far-reaching consequences. The main result may also be viewed as a Lipschitz
regularity result for the Beltrami equation, and so for certain planar second
order elliptic equations in divergence form.
