Quantization is an essential mechanism in analog‐to‐digital conversion and proper design of the quantizer to minimize quantization error is important to digital signal processing systems. Many cost functions have been proposed as the distortion measure for the actual design of a quantizer, and non‐mean‐squared error criteria are often presented as physically significant. One of the non‐mean‐squared error criteria frequently discussed is the meanrth power error distortion measure. In this paper efficient methods for the design of minimum meanrth power error quantizers are presented and demonstrated by numerical examples. A closed form solution of minimum mean absolute error quantization for‐ Laplace‐distributed signals is also provided. Compared with previous work, the simple algorithms discussed in this paper are more accurate.