  The redundancy for universal lossless compression of discrete memoryless
sources in Campbell's setting is characterized as a minimax R\'enyi divergence,
which is shown to be equal to the maximal $\alpha$-mutual information via a
generalized redundancy-capacity theorem. Special attention is placed on the
analysis of the asymptotics of minimax R\'enyi divergence, which is determined
up to a term vanishing in blocklength.
