Consider a receiver that observes multiple interfering codewords. The compute-and-forward technique makes it possible for the receiver to directly decode linear combinations of the codewords. Previous work has focused on compute-and-forward for linear Gaussian networks. This paper explores the corresponding technique for discrete memoryless networks. As a by-product, this leads to a novel way of attaining non-trivial points on the dominant face of the capacity region of discrete memoryless multiple-access channels.