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The accuracy of time-domain solutions of the inhomogeneous Teukolsky equationis improved significantly. Comparing energy fluxes in gravitational waves withhighly accurate frequency-domain results for circular equatorial orbits inSchwarzschild and Kerr, we find agreement to within 1% or better, which webelieve can be even further improved. We apply our method to orbits for whichfrequency-domain calculations have a relative disadvantage, specificallyhigh-eccentricity (elliptical and parabolic) "zoom-whirl" orbits, and find theenergy fluxes, waveforms, and characteristic strain in gravitational waves.Comment: 6 pages, 9 figures, 2 tables; Changes: some errors corrected.  Comparison with Frequency-domain now done in stronger fiel

Accurate time-domain gravitational waveforms for extreme-mass-ratio binaries