A growing research line documents significant bivariate correlations between individual measures of speech perception gathered in infancy and concurrent or later vocabulary size. One interpretation of this correlation is that it reflects language specificity: Both speech perception tasks and the development of the vocabulary recruit the "same" linguistic modules. However, correlations between infant cognitive measures (such as visual recognition memory) and vocabulary are also significant and display comparable strength. Can all of these correlations be reduced to extremely general rather than "specific" factors affecting performance in all laboratory tests? We take a first step in addressing this possibility by estimating the covariance matrix among two speech tasks (preference for the predominant stress pattern and native vowel discrimination) and two cognitive tasks (visual recognition memory and A-not-B), all of them gathered in the same group of infants tested between 5 and 8 months of age. Only the correlation between the two speech tasks was significant, lending little support to the generalist explanation. These data illustrate how a multivariate approach may inform our understanding of how infants build language in the first year of life and beyond. Future multivariate work following up on the same infants longitudinally will be better able to tease apart cognitive and linguistic contributions to vocabulary development.