Using double-resonance conditions, in which the Larmor frequency of a spin-1/2 nucleus is matched to one of the nuclear quadrupole resonance frequencies of a spin-1 nucleus, the authors demonstrate increased cross relaxation between the two nuclear spin species. They calculate the cross-relaxation rate using the motionally averaged heterogeneous dipole Hamiltonian as a perturbation to the combined quadrupole and Zeeman Hamiltonians. Using this cross-relaxation rate, in addition to hydrogen and nitrogen autorelaxation rates, expressions governing spin-1/2 and spin-1 spin-lattice relaxation are determined. With ammonium nitrate, containing nitrogen (spin-1) and hydrogen (spin-1/2), increased nitrogen signal and spin-lattice relaxation are demonstrated, using fields less than 120 G. The cross-relaxation rate is also measured and an overall signal/noise improvement by a factor of 2.3+/-0.1 is attained.