We report results from children learning to read in one of four different languages: Croatian, English, Estonian and Swedish. The languages all have an alphabetical script but vary greatly on the dimension deep-shallow (or complexity-simplicity, or opacity-transparency), i.e., how close orthography and phonology are related. These languages also vary in the complexity and type of grammatical structure. We used tasks to measure phonological awareness, morpho-syntactic processing, word and pseudoword identification speed, working memory, and reading comprehension. In English, Swedish, and Croatian, fluency was the most significant predictor of reading comprehension. In Estonian, morpho-syntactic awareness was the most significant predictor, although reading fluency was a close second. Fluency was of primary importance in reading comprehension because the limitations of working memory result in fast decay of input information. Therefore, it is important to read with fluency for proper text comprehension.