  A code of the natural numbers is a uniquely-decodable binary code of the
natural numbers with non-decreasing codeword lengths, which satisfies Kraft's
inequality tightly. We define a natural partial order on the set of codes, and
show how to construct effectively a code better than a given sequence of codes,
in a certain precise sense. As an application, we prove that the existence of a
scale of codes (a well-ordered set of codes which contains a code better than
any given code) is independent of ZFC.
