We studied how statistical models of morphology that are built on different kinds of representational units, i.e., models emphasizing either holistic units or decomposition, perform in predicting human word recognition. More specifically, we studied the predictive power of such models at early vs. late stages of word recognition by using eye-tracking during two tasks. The tasks included a standard lexical decision task and a word recognition task that assumedly places less emphasis on postlexical reanalysis and decision processes. The lexical decision results showed good performance of Morfessor models based on the Minimum Description Length optimization principle. Models which segment words at some morpheme boundaries and keep other boundaries unsegmented performed well both at early and late stages of word recognition, supporting dual- or multiple-route cognitive models of morphological processing. Statistical models based on full forms fared better in late than early measures. The results of the second, multi-word recognition task showed that early and late stages of processing often involve accessing morphological constituents, with the exception of short complex words. Late stages of word recognition additionally involve predicting upcoming morphemes on the basis of previous ones in multimorphemic words. The statistical models based fully on whole words did not fare well in this task. Thus, we assume that the good performance of such models in global measures such as gaze durations or reaction times in lexical decision largely stems from postlexical reanalysis or decision processes. This finding highlights the importance of considering task demands in the study of morphological processing.