Current neural network-based conversational models lack diversity and generate boring responses to open-ended utterances. Priors such as persona, emotion, or topic provide additional information to dialog models to aid response generation, but annotating a dataset with priors is expensive and such annotations are rarely available. While previous methods for improving the quality of open-domain response generation focused on either the underlying model or the training objective, we present a method of filtering dialog datasets by removing generic utterances from training data using a simple entropy-based approach that does not require human supervision. We conduct extensive experiments with different variations of our method, and compare dialog models across 17 evaluation metrics to show that training on datasets filtered this way results in better conversational quality as chatbots learn to output more diverse responses.