  We prove the corona theorem for domains whose boundary lies in certain smooth
quasicircles. These curves, which are not necessarily Dini-smooth, are defined
by quasiconformal mappings whose complex dilatation verifies certain
conditions. Most importantly we do not assume any "thickness" condition on the
boundary domain. In this sense, our results complement those obtained by
Garnett and Jones (1985) and C. Moore on $C^{1+\alpha}$ curves (1987).
