The studies of tobacco demand accounting for product diversity haveattracted much attention in the literature, but theex antemeasurements ofthe effects of product bans are relatively scarce. This paper aims to fill this gapand considers the 2020 EU-induced ban on menthol cigarettes as an example,focusing on the Polish market. In the proposed approach, a 2004-2017 product-level dataset for Poland is used to estimate a random coefficients logit modeland simulate the effects of the menthol ban and, for comparison, a cigaretteexcise hike. The dataset is unique as it encompassess substantial changes inthe tobacco tax level and structure that took place in Poland over the sampleperiod. The simulations suggest that the ban, despite switching of consumerstowards non-menthol cigarettes, results in relatively strong reduction in demandfor duty-paid cigarettes, stronger than in the case of the excise hike.