Bar charts with y-axes that don't begin at zero can visually exaggerate effect sizes. However, advice for whether or not to truncate the y-axis can be equivocal for other visualization types. In this paper we present examples of visualizations where this y-axis truncation can be beneficial as well as harmful, depending on the communicative and analytic intent. We also present the results of a series of crowd-sourced experiments in which we examine how y-axis truncation impacts subjective effect size across visualization types, and we explore alternative designs that more directly alert viewers to this truncation. We find that the subjective impact of axis truncation is persistent across visualizations designs, even for designs with explicit visual cues that indicate truncation has taken place. We suggest that designers consider the scale of the meaningful effect sizes and variation they intend to communicate, regardless of the visual encoding.