Reading speed is commonly used as an index of reading fluency. However, reading speed is not a consistent predictor of text comprehension, when speed and comprehension are measured on the same text within the same reader. This might be due to the somewhat ambiguous nature of reading speed, which is sometimes regarded as a feature of the reading process, and sometimes as a product of that process. We argue that both reading speed and comprehension should be seen as the result of the reading process, and that the process of fluent text reading can instead be described by complexity metrics that quantify aspects of the stability of the reading process. In this article, we introduce complexity metrics in the context of reading and apply them to data from a self-paced reading study. In this study, children and adults read a text silently or aloud and answered comprehension questions after reading. Our results show that recurrence metrics that quantify the degree of temporal structure in reading times yield better prediction of text comprehension compared to reading speed. However, the results for fractal metrics are less clear. Furthermore, prediction of text comprehension is generally strongest and most consistent across silent and oral reading when comprehension scores are normalized by reading speed. Analyses of word length and word frequency indicate that the observed complexity in reading times is not a simple function of the lexical properties of the text, suggesting that text reading might work differently compared to reading of isolated word or sentences.