The introduction of a centralized institution for trading production rights in quota-regulated agricultural sectors can dramatically improve the flow of information among market participants and increase efficiency. On the other hand, prevailing conditions in these small markets can provide sellers with a market advantage, yielding high quota prices that impose important financial costs on quota holders and limit the entry of new producers into the industry. In this paper, we modify the normal allocation rule of the k-double auction (kDA) to counter thin market conditions and to favor buyers who bid low prices. In laboratory experiments, we test the “truncated” kDA (T-kDA) against a regular kDA for its ability to affect buyer and seller behavior and decrease equilibrium prices, and assess how it impacts efficiency. The results show that the T-kDA significantly lowers the equilibrium price and results in moderate efficiency losses. Most importantly, the T-kDA effectively counters the market power of oligopolists when demand far outstrips supply.