A current theoretical view proposes that infants converge on the speech categories of their native language by attending to frequency distributions that occur in the acoustic input. To date, the only empirical support for this statistical learning hypothesis comes from studies where a single, salient dimension was manipulated. Additional evidence is sought here, by introducing a less salient pair of categories supported by multiple cues. We exposed English-learning infants to a multi-cue bidimensional grid between retroflex and alveolopalatal sibilants in prevocalic position. This contrast is substantially more difficult according to previous cross-linguistic and perceptual research, and its perception is driven by cues in both the consonantal and the following vowel portions. Infants heard one of two distributions (flat, or with two peaks), and were tested with sounds varying along only one dimension. Infants' responses differed depending on the familiarization distribution, and their performance was equally good for the vocalic and the frication dimension, lending some support to the statistical hypothesis even in this harder learning situation. However, learning was restricted to the retroflex category, and a control experiment showed that lack of learning for the alveolopalatal category was not due to the presence of a competing category. Thus, these results contribute fundamental evidence on the extent and limitations of the statistical hypothesis as an explanation for infants' perceptual tuning.