Children’s language input is rife with acoustic variability. Much of this variability may facilitate learning by highlighting unvarying, criterial speech attributes. But in many cases, learners experience variation in those criterial attributes themselves, as when hearing speakers with different accents. How flexible are children in the face of this variability? The current study taught 3–5-year-olds new words containing speech-sound variability: a single picture might be labeled both deev and teev. After learning, children’s knowledge was tested by presenting two pictures and asking them to point to one. Picture-pointing accuracy and eye movements were tracked. While children pointed less accurately and looked less rapidly to dual-label than single-label words, they robustly exceeded chance. Performance was weaker when children learned two distinct labels, such as vayfe and fosh, for a single object. Findings suggest moderate learning even with speech-sound variability. One implication is that neural representations of speech contain rich gradient information.