We study twist-three effects in spin, charge, and azimuthal asymmetries in
deeply virtual Compton scattering on a spin-zero target. Contributions whic
h are power suppressed in 1/Q generate a new azimuthal angle dependence of
the cross section that is not present in the leading twist results. On the
other hand, the leading twist terms are not modified by the twist-three con
tributions. They may get corrected at the twist-four level, however. In the
Wandzura-Wilczek approximation these new terms in the Fourier expansion wi
th respect to the azimuthal an le are entirely determined by the twist-two
generalized parton distributions. We also discuss more general issues such
as the general form of the angular dependence of the differential cross sec
tion, the validity of factorization at the twist-three level, and the relat
ion of generalized parton distributions to spectral functions.