  We compute dijet production in Deep Inelastic Scattering at low $x$ in the
dipole formalism at next-to-eikonal accuracy. We calculate the contributions
induced by single photon exchange of either longitudinal or transverse
polarization. We include all types of corrections to the eikonal approximation
in the gluon background field: (i) finite longitudinal width of the target,
(ii) interaction of the quark-antiquark pair with the subleading (transverse)
component of the background field and (iii) dynamics of the target which is
encoded in the $z^-$-coordinate dependence of the background field. The final
expressions for the dijet cross section are written as sum of a "generalized
eikonal" contribution (where longitudinal momentum $p^+$ exchange between the
target and the incoming quark-antiquark pair is allowed since the average $z^-$
dependence of the background field is kept) and explicit next-to-eikonal
corrections that involve decorated dipole and quadrupole operators.
