We study the design of credit default swaps (CDS) auctions, which determine the payments by CDS sellers to CDS buyers following defaults of bonds. Using a simple model, we find that the current design of CDS auctions leads to biased prices and inefficient allocations. This is because various restrictions imposed in CDS auctions prevent certain investors from participating in the price discovery and allocation process. The imposition of a price cap or floor also gives dealers large influence on the final auction price. We propose an alternative double auction design that delivers more efficient price discovery and allocations.