A major goal in the early years of elementary school is learning to read, a process in which children show substantial individual differences. To shed light on the underlying processes of early literacy, this study investigates the interrelations among four known precursors to literacy: phonological short-term memory, vocabulary size, rhyme awareness, and trainability in the phonological specificity of lexical representations, by means of structural equation modelling, in a group of 101 4-year-old children. Trainability in lexical specificity was assessed by teaching children pairs of new phonologically-similar words. Standardized tests of receptive vocabulary, short-term memory, and rhyme awareness were used. The best-fitting model showed that trainability in lexical specificity partially mediated between short-term memory and both vocabulary size and rhyme awareness. These results demonstrate that individual differences in the ability to learn phonologically-similar new words are related to individual differences in vocabulary size and rhyme awareness.