Proponents of ‘usage-based’ models [Bybee, J.L., 1995. Regular morphology and the lexicon. Language and Cognitive Processes 10, 425–455; Langacker, R.W., 2000. A dynamic usage-based model. In: Barlow, M., Kemmer, S. (Eds.), Usage-Based Models of Language. CSLI Publications, Stanford, CA, pp. 1–63; Tomasello, M., 2003. Constructing a Language: A Usage-Based Theory of Child Language Acquisition. Harvard University Press, Cambridge, MA] have argued that speakers’ mental grammars are highly redundant, in that relatively specific, low-level generalizations and actual expressions co-exist with more general rules. Such local generalizations are thought to play an important role in language use, and, in particular, in language acquisition. If this hypothesis is correct, speakers, and especially immature speakers, should be more likely to supply the correct inflected forms of words which fall into densely populated phonological neighbourhoods (for which they are likely to have extracted low-level schemas) than with words with few neighbours (for which no low-level schemas may be available). This paper tests this prediction by investigating Polish children’s ability to supply case inflections with unfamiliar words. By far the most densely populated regions in Polish children’s noun lexicons are those defined by the three most productive diminutive suffixes (masculine -ek, feminine -ka, and neuter -ko), since diminutives are very frequent in the input. Therefore, if the low-level schema hypothesis is correct, children should be more productive with diminutives and diminutive-sounding words (i.e., words ending in -ek, -ka, and -ko) than with simplex forms. Results indicate that this is indeed the case.