We study black-hole binaries in the intermediate-mass-ratio regime 0.01≲q≲0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the leading and nonleading (ℓ, m) modes. As a proof-of-concept, we compute waveforms for q=1/10. We discuss applications of these techniques for LIGO and VIRGO data analysis and the possibility that our technique can be extended to produce accurate waveform templates from a modest number of fully nonlinear numerical simulations.