The Payment for Insufficient Density is an innovative measure that has made its entry into French law recently. It enables mayors to require real estate developers to settle a certain amount of money in the case where the floor-area ratio of a new building does not meet a defined Minimum Density Threshold. Such a policy aims to mitigate urban sprawl, but its potential consequences on housing supply and the revenues it can generate are not easy to anticipate. Using a land-use transport interaction-model (NEDUM 2D) calibrated on Paris urban area, we have investigated the potential impacts of such a policy, and analyzed how it can be best used to gain efficiency, while keeping social costs low. It is found that, if appropriately implemented, it can limit urban sprawl, and, at the same time increase overall housing supply, therefore contributing to decrease average rent or real estate price levels. Surprisingly, the Payment for Insufficient Density by taxing construction can thus lead to an increase in total floor space. However, implementing such a policy can be tricky, as the choice of the Minimum Density Threshold conditions its efficiency in a non-trivial way. If the chosen threshold is too low, for example because mayors want to limit the tax burden weighing on construction firms, it can even have counter-productive effects such as an acceleration of urban sprawl. Furthermore, depending on the prime objective of the policy, such as, for example, limiting urban sprawl, maximizing access to public transport or decreasing commuting distances, the choice of the optimal threshold will vary.