Humans tend to follow the Uniform Information Density (UID) principle by distributing information evenly in utterances. We study if decoding algorithms implicitly follow this UID principle, and under what conditions adherence to UID might be desirable for dialogue generation. We generate responses using different decoding algorithms with GPT-2 on the Persona-Chat dataset and collect human judgments on their quality using Amazon Mechanical Turk. We find that (i) surprisingly, model-generated responses follow the UID principle to a greater extent than human responses, and (ii) decoding algorithms that promote UID do not generate higher-quality responses. Instead, when we control for surprisal, non-uniformity of information density correlates with the quality of responses with very low/high surprisal. Our findings indicate that encouraging non-uniform responses is a potential solution to the “likelihood trap” problem (quality degradation in very high-likelihood text). Our dataset containing multiple candidate responses per dialog history along with human-annotated quality ratings is available at: https://huggingface.co/datasets/saranya132/dialog_uid_gpt2.