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Language models (LMs) are often constructed by building component models on multiple text sources to be combined using global, context free interpolation weights. By re-adjusting these weights, LMs may be adapted to a target domain representing a particular genre, epoch or other higher level attributes. A major limitation with this approach is other factors that determine the usefulness of sources on a context dependent basis, such as modeling resolution, generalization, topics and styles, are poorly modeled. To overcome this problem, this paper investigates a context dependent form of LM interpolation and test-time adaptation. Depending on the context, a discrete history weighting function is used to dynamically adjust the contribution from component models. In previous research, it was used primarily for LM adaptation. In this paper, a range of schemes to combine context dependent weights obtained from training and test data to improve LM adaptation are proposed. Consistent perplexity and error rate gains of 6% relative were obtained on a state-of-the-art broadcast recognition task.