The pattern of financial linkages is important in many areas of banking and finance. Yet bilateral linkages are often unknown, and maximum entropy serves as the leading method for estimating unobserved counterparty exposures. This paper proposes an efficient alternative that combines information-theoretic arguments with economic incentives to produce more realistic interbank networks that preserve important characteristics of the original interbank market. The method loads the most probable links with the largest exposures consistent with the total lending and borrowing of each bank, leading to networks with minimum density. When used in a stress testing context, the minimum density approach performs better than maximum entropy and also permits more robust analysis. Using the two benchmarks side by side helps identify a range of possible systemic risk outcomes when the true pattern of counterparty exposures is unknown.