A number of estimates are available for the extraction of rain rate from the measurements of an attenuating frequency radar. The estimates, which arise from various approximations for the attenuation, include at one extreme the estimate in which no correction for attenuation is made. An infinite number of higher-order estimates exist which are shown in the limit to approach the Hitschfeld-Bordan solution. An error analysis is carried out for four of the estimates, taking into account the various "system" errors which include the randomness of the radar return power and the k-Z, Z-R relations as well as the offsets in the radar calibration constant. The results indicate that as these errors are more narrowly bracketed, progressively higher-order estimates can be beneficially employed. However, since the behavior of the estimates is strongly dependent on the system errors, the choice of the best estimate may be difficult without an accurate specification of these errors. Furthermore, in order for any of the estimates to provide a reliable means of rain-rate prediction in the presence of realistic errors, the attenuation must be kept small. This is usually insured for antenna pointing angles away from the horizontal at radar frequencies at the lower end of the X-band.