This article studies the impact of competition on the degree of inefficiency in lemons markets. More precisely, we characterise the second‐best mechanism (i.e. the optimal mechanism with private information) in a stylised lemons market with finite numbers of buyers and sellers. We then study the relationship between the degree of efficiency of the second‐best mechanism and market competitiveness. A general message of our results is that increasing competition may not help lemons markets in some circumstances. Moreover, increasing competition beyond a certain degree increases the distance between the first‐best and second‐best levels of efficiency.