Waste paper is recovered and bleached to produce recycled newsprints and magazines. It is composed of a fibre mixture from different wood pulping processes. Each type of fibre shows a different reactivity towards bleaching. Consequently, if the composition of waste paper changes over time, the actual industrial bleaching process may no longer be suitable to achieve the intended brightness. This study aims to develop a multiple linear regression that correlates brightness and fibre composition to determine in advance whether a waste paper stream can achieve the intended brightness. Several samples of four of the most representative fibre types were bleached under specific laboratory conditions, and the resulting brightness was used to develop the regression. The resulting model is valid and consistent when the amount of bleached fibre chemically pulped type in the mixed fibre stream does not exceed 80%. Waste samples with a known fibre composition were then bleached to verify the model. The measured brightness followed the same trend predicted by the regression but was lower at a constant value. The use of a correction factor allowed for a good fit. The cause of this discrepancy could be the differences between the reference fibre mixtures and waste paper pulp not included in the model (e.g. contaminants or collapsed fibres). This work is a first step to develop a simple statistical tool to estimate the brightness of waste paper pulp, despite some limitations.