Given that words from the academic layer of English typically carry bound roots ("min" in "diminish") rather than free-standing base words ("small" in "smaller"), there is a need to understand the factors that make bound roots more or less accessible for morphological problem-solving unfamiliar words. We investigated the contributions of learner characteristics and morpheme/word characteristics to the morphological problem-solving skill of 87 language minority learners. Participants analyzed 18 morphologically complex, unfamiliar words on a Morphological Analysis Task. Among learner characteristics, results from multilevel logistic models indicated that only English proficiency predicted difficulty. For root characteristics, semantic opaqueness, phonological shift, and orthographic neighborhood size predicted difficulty as expected. Morphological family size also predicted difficulty, but in unexpected ways, with larger family size predicting greater difficulty. Exploratory analyses suggested that family size may interact with other root characteristics to further influence difficulty. Findings hold implications for models of morphological processing and literacy intervention design.