We are analysing Stockholm, Sweden’s regulated rental housing market, by analysing the distribution of rental apartments based on a person’s position in the housing agency queue. Our objective is to examine queue times and estimate the demand for rent-regulated apartments, as well as the market’s income elasticity. Using the hedonic two-step approach, we use empirical data from rental contracts provided by the Stockholm Housing Agency to investigate the relationship between individual waiting times and their characteristics, such as income, age, and family composition. The empirical analysis found a strong willingness to pay for rent-regulated apartments, especially for larger homes in better locations with lower regulated rent. The demand for rental apartments increases with increasing income, but this effect is less pronounced in the current distribution system. The findings will be valuable to real estate developers, property owners, and city planners to improve policies for the rental housing market.