We present a new, high-resolution (1".8) determination of the 5-1.5 GHz radio spectral index (alpha(1.5-5 GHz)) of the Crab Nebula based on the recent radio observations by Bietenholz and Kronberg. We also present a 1.5-14 GHz spectral index image of the Crab with 6".5 resolution. Small-scale, variable, wisp-like features are found near the center of the Crab nebula which exhibit a spectral index flatter (by 0.05 +/- 0.01) than that of the rest of the nebula. They are part of an apparently organized complex of alpha perturbations which appear as tilted ring-like features having thickness less-than-or-equal-to 0.01 pc and diameter of order 0.6 pc. The more intense parts of these alpha features are also visible in total emission and seem to be associated with the highly variable features visible in the optical continuum (Scargle's wisps) although an exact positional coincidence is unlikely. They are seen to change both in intensity and position over the period 1982-1985. No variation in alpha is seen at the locations of the bright, optical line emitting filaments (DELTA-alpha(1.5-5 GHz) < 0.02) up to 14 GHz. Litle, if any large-scale variation in the Crab's alpha(1.5-5 GHz) is found. In particular, the outside edge of the nebula exhibits an alpha(1.5-5 GHz) within 0.05 of that of the rest of the nebula.
