Cumulative initial-state-selected cross sections for the H + D-2(nu,j) --> HD + D reaction are presented. Initial states with vibrational quantum numbers nu=0,1 and rotational quantum numbers j=0-4, and initial translational energies up to 2.5 eV are considered. These calculations go beyond previous ones in treating higher energies and vibrationally excited D-2. The cross sections are computed by propagating wave packets employing the multiconfiguration time-dependent Hartee scheme, and by analyzing the reactive flux into the configuration channel of the products. The initial wave packets are modified to account for the long-range part of the potential, assuming vibrational adiabaticity. All calculations are performed within the coupled states approximation on the Liu-Siegbahn-Truhlar-Horowitz (LSTH) potential-energy surface. The LSTH surface is expanded in products of one-dimensional functions of the Jacobian coordinates. The initial-state-selected cross sections are averaged over a room-temperature Boltzmann distribution of the D2 rotational states to compare the results with experimentally observed values. The relative efficiency of vibrational, rotational, and translational energy for promoting the reaction is analyzed.