The Common Core set a standard for all children to read increasingly complex texts throughout schooling. The purpose of the present study was to explore text characteristics specifically in relation to early-grades text complexity. Three hundred fifty primary-grades texts were selected and digitized. Twenty-two text characteristics were identified at 4 linguistic levels, and multiple computerized operationalizations were created for each of the 22 text characteristics. A researcher-devised text-complexity outcome measure was based on teacher judgment of text complexity in the 350 texts as well as on student judgment of text complexity as gauged by their responses in a maze task for a subset of the 350 texts. Analyses were conducted using a logical analytical progression typically used in machine-learning research. Random forest regression was the primary statistical modeling technique. Nine text characteristics were most important for early-grades text complexity including word structure (decoding demand and number of syllables in words), word meaning (age of acquisition, abstractness, and word rareness), and sentence and discourse-level characteristics (intersentential complexity, phrase diversity, text density/information load, and noncompressibility). Notably, interplay among text characteristics was important to explanation of text complexity, particularly for subsets of texts.