This article offers an account of i-umlaut in Old English based on lexical minimality: the elimination of redundancies from, in this case, the phonological subentries in the lexicon. And the notation is that of Anderson & Ewen (1987), which is based, crucially for the present formulation, on simplex features which may combine in varying proportions. These assumptions combine to favour system-dependent underspecification. In accord with lexical minimality, the approach taken here is also polysystemic: thus, for instance, Old English vowels, even Old English accented vowels, do not enter into only one system of contrasts. The phonology is a system of systems sharing some but not all contrasts. The article attempts to show that on this basis some of the many apparent anomalies that the evidence has been thought to suggest can be resolved in terms of a simple coherent formulation. Concerning the interpretation of this evidence, it is the intention of the article to minimize appeals to phonetic features and phonetic processes not warranted by textual and comparative testimony. It is suggested that lack of attention to polysystemicity and a pervasive indulgence on the part of historical phonologists in phonetic fantasies undermine the conclusions reached by generations of scholars concerning the development of phonological systems, both in general and in particular.