We contribute to the literature on undesirable-output technology modeling by first discussing the limits of the recently proposed by-production approach of Murty et al. (2012) (hereafter we will refer to these authors as MRL) and second by proposing some possible extensions. We identify two theoretical limits and two practical drawbacks when using Data Envelopment Analysis (DEA) with this approach. Theoretically, MRL’s by-production model is based on estimating two sub-technologies, one representing good outputs and the other one representing undesirable outputs. However, MRL assume independence of the sub-frontiers. In our paper, by contrast, we discuss the importance and implications of considering that all production processes are interconnected and should not be considered separately. Among the three extensions proposed, we argue that the introduction of some dependence constraints that link the two sub-technologies considered in this framework is very powerful. The two by-production approaches, MRL’s and ours, are discussed under the restrictive assumption of fixed levels of inputs and under the flexible case of free choice of polluting input quantities. An application to a sample of 112 countries reveals that MRL model gives higher inefficiency scores compared to our extension with dependence constraints.