We tested current models of morphological processing in reading with data from four visual lexical decision experiments using German compounds and monomorphemic words. Triplets of two semantically transparent noun-noun compounds and one monomorphemic noun were used in Experiments 1a and 1b. Stimuli within a triplet were matched for full-form frequency. The frequency of the compounds' constituents was varied. The compounds of a triplet shared one constituent, while the frequency of the unshared constituent was either high or low, but always higher than full-form frequency. Reactions were faster to compounds with high-frequency constituents than to compounds with low-frequency constituents, while the latter did not differ from the monomorphemic words. This pattern was not influenced by task difficulty, induced by the type of pseudocompounds used. Pseudocompounds were either created by altering letters of an existing compound (easy pseudocompound, Experiment 1a) or by combining two free morphemes into a non-existing, but morphologically legal, compound (difficult pseudocompound, Experiment 1b). In Experiments 2a and 2b, frequency-matched pairs of semantically opaque noun-noun compounds and simple nouns were tested. In Experiment 2a, with easy pseudocompounds (of the same type as in Experiment 1a), a reaction-time advantage for compounds over monomorphemic words was again observed. This advantage disappeared in Experiment 2b, where difficult pseudocompounds were used. Although a dual-route might account for the data, the findings are best understood in terms of decomposition of low-frequency complex words prior to lexical access, followed by processing costs due to the recombination of morphemes for meaning access. These processing costs vary as a function of intrinsic factors such as semantic transparency, or external factors such as the difficulty of the experimental task.