Input is considered one of the most important factors in the acquisition of lexical and grammatical skills. Input has been found to interact with other factors, such as learner cognitive skills and the circumstances where language is heard. Language learning itself has sometimes been found to enhance cognitive skills. Indeed, intensive contact with another language has been found to sometimes boost cognitive skills, even in intensive instructed settings, such as immersion programs (bilingual advantage hypothesis). In this paper, we report a cross-sectional study to assess grammar learning of 79 fourth grade German students learning L2 English in two immersion schools. Verbal teacher input was assessed using the Teacher Input Observation Scheme (TIOS, Items 14-25), and the learners' L2 grammar comprehension was tested with the ELIAS Grammar Test II. Cognitive skills, including phonological awareness, working memory, and non-verbal intelligence, were determined using standardized assessment procedures. The results show that verbal input quantity and quality correlated significantly with the learners' L2 grammar comprehension. None of the cognitive skills moderated the effect of input on grammar comprehension but all predicted it independently. The combination of L2 input and phonological awareness was found to be the most robust predictor of L2 grammar comprehension.