The specific differential phase shift on propagation K_dp is widely employed in the study of precipitation, although little is known about the effective accuracy of its estimates. The aim of this letter is to analyze the quality of K_dp estimates, using realistic simulated fields of drop size distributions. Two classical and one recently proposed estimation algorithms are tested, which are chosen among the algorithms that use the measured and noisy total differential phase shift Ψ_dp as their main input. A data set of six simulated rain events, from which polarimetric radar variables can be derived, is employed in this letter. The mean normalized absolute error in the estimation of K_dp at the radar resolution volume scale ranges from 27% to 30% for all the algorithms proposed, and significant negative biases up to -50% emerge at the highest values of K_dp for the most biased algorithm. The new algorithm, which is based on Kalman filtering, is able to keep these localized bias values around -25% and outperforms the classical algorithms in terms of efficiency, correlation, and root-mean-square error.