The structure of lexical entries and the status of lexical decomposition remain controversial. In the psycholinguistic literature, one aspect of this debate concerns the psychological reality of the morphological complexity difference between compound words ("teacup") and single words ("crescent"). The present study investigates morphological decomposition in compound words using visual lexical decision with simultaneous magnetoencephalography (MEG), comparing compounds, single words, and pseudomorphemic foils. The results support an account of lexical processing which includes early decomposition of morphologically complex words into constituents. The behavioural differences suggest internally structured representations for compound words, and the early effects of constituents in the electrophysiological signal support the hypothesis of early morphological parsing. These findings add to a growing literature suggesting that the lexicon includes structured representations, consistent with previous findings supporting early morphological parsing using other tasks. The results do not favour two putative constraints, word length and lexicalisation, on early morphological-structure based computation. (Contains 8 figures, 7 tables and 17 footnotes.)