This correspondence presents entropy analyses for dithered and undithered quantized sources. Two methods are discussed that reduce the increase in entropy caused by the dither. The first method supplies the dither to the lossless encoding-decoding scheme. It is argued that this increases the complexity of the encoding-decoding scheme. A method to reduce this complexity is proposed. The second method is the usage of a dead-zone quantizer. A procedure for determining the optimal dead-zone width in the mean-square sense is given