Summary: The data envelopment analysis technique produces higher efficiency scores for the assessed decision making units (DMUs) when more input/output factors are considered. This feature generates an intuitively unreasonable result in which the efficiency of a DMU measured considering the accompanying undesirable outputs is greater than or equal to that measured without considering them. In order to obtain a reasonable measure of efficiency, this paper proposes a concept for determining the minimum amount of undesirable outputs that a DMU is allowed to generate based on the assertion of weak disposability, and the results are used to construct the production frontier. The efficiency of the DMUs measured from this frontier can be decomposed into two parts, one of which shows the efficiency of consuming the observed inputs to produce the observed desirable outputs and the other of which, a reduction factor, shows the effect of producing excessive amounts of undesirable outputs on efficiency. A case of thirty paper mills taken from the literature is used to illustrate this idea. The results are helpful for DMU decision-makers to identify sources of inefficiency and for the government to formulate standards for generating allowable amounts of undesirable outputs.