The Smooth Signal Redundancy Hypothesis explains variations in syllable length as a means to more uniformly distribute information throughout the speech signal. The Uniform Information Density hypothesis seeks to generalize this to choices on all linguistic levels, particularly syntactic choices. While there is some evidence for the Uniform Information Density hypothesis, it faces several challenges, four of which are discussed in this paper. First, it is not clear what exactly counts as uniform. Second, there are syntactic alternations that occur systematically but that can cause notable fluctuations in the information signature. Third, there is an increasing body of negative results. Fourth, there is a lack of large-scale evidence. As to the fourth point, this paper provides a broader array of data-936 sentence pairs for nine syntactic constructions-and analyzes them in a test setup that treats the hypothesis as a classifier. For our data, the Uniform Information Density hypothesis showed little predictive capacity. We explore ways to reconcile our data with theory.