We present IR surface brightness fluctuation (SBF) distance measurements to NGC 4889 in the Coma cluster and to NGC 3309 and NGC 3311 in the Hydra cluster. We explicitly corrected for the contributions to the fluctuations from globular clusters, background galaxies, and residual background variance. We measured a distance of 85 +/- 10 Mpc to NGC 4889 and a distance of 46 +/- 5 Mpc to the Hydra cluster. Adopting recession velocities of 7186 +/- 428 km/s for Coma and 4054 +/- 296 km/s for Hydra gives a mean Hubble constant of H_0 = 87 +/- 11 km/s/Mpc. Corrections for residual variances were a significant fraction of the SBF signal measured, and, if underestimated, would bias our measurement towards smaller distances and larger values of H_0. Both NICMOS on the Hubble Space Telescope and large-aperture ground-based telescopes with new IR detectors will make accurate SBF distance measurements possible to 100 Mpc and beyond.

24 pages, 4 PostScript figures, 2 JPEG images; accepted for publication in ApJ