  We present the first calculation of inclusive jet production in
deep-inelastic scattering with approximate next-to-next-to-leading order
(aNNLO) contributions, obtained from a unified threshold resummation formalism.
The leading coefficients are computed analytically. We show that the aNNLO
contributions reduce the theoretical prediction for jet production in
deep-inelastic scattering, improve the description of the final HERA data in
particular at high photon virtuality Q^2 and increase the central fit value of
the strong coupling constant.
