In environmental assessment studies, the economic principle of weak disposability plays a significant role employing Data Envelopment Analysis (DEA).World commissions on the environment protection asserts that reducing undesirable (bad) outputs often demand employing the concept of weak disposability instead of free disposability assumptions. A model proposes in this paper, calculate the proportional reduction threshold of undesirable outputs from a production unit using weak disposability. Furthermore, in the proposed model, the reduction level of undesirable output is dependent to the desirable output decrement. The model utilizes the form of weak disposability enables each production unit to have non uniform abatement factor reducing undesirable and desirable outputs together. It is shown that the proposed model can determine the required level of reduction for undesirable outputs in the production process contributing the adoption of more rigorous regulation to protect the environment. The model is analyzed employing real data from 30 paper miles in China.