We describe a new method for pruning in dynamic models based on running an adaptive filtering algorithm online during decoding to predict aspects of the scores in the near future. These predictions are used to make well-informed pruning decisions during model expansion. We apply this idea to the case of dynamic graphical models and test it on a speech recognition database derived from Switchboard. Results show that significant (approximately factor of 2) speedups can be obtained without any decrease in word error rate or increase in memory usage.