The design of an optimum quantizer can be formulated as an optimization problem that finds the quantization indices that minimize the quantization error. One solution of the optimization problem is DP quantization, an approach based on dynamic programming. It is known that a quantized signal does not always contain signal values that can be represented with a given bit-depth. This property is called amplitude sparseness. Because quantization is the amplitude discretization of signal value, amplitude sparseness is closely related to the design of the quantizer. Since signal values with zero frequency do not affect quantization error, there is the potential to reduce complexity when designing the optimum quantizer by skipping the processing of signal values that have zero frequency. However, conventional methods on DP quantization do not design for amplitude sparseness and so are unduly complex. In this paper, we propose an algorithm that yields an optimum quantizer that minimizes quantization error with reduced complexity given the existence of amplitude sparseness.