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This paper investigates vowel changes from Old English to Middle English, especially focusing on the change of /ü:/ and /ü/ and accounts for the sound change within a constraint-based framework. The Middle English vowels /ü:/ and /ü/ are divided into three kinds of pronunciation based on dialects. The dialectal changes of /ü:/ and /ü/ finally result in merger with the vowel /i/. In other languages /ü:/ and /ü/ are changed to [u:] and [u] respectively (e.g., in White Hmong). In the case of a rule-based theory, the former needs unrounding and the latter needs vowel-backing. These two language- specific rules (unrounding, vowel-backing) aim at just one common goal (maximizing ease of articulation). They conspire to avoid high front rounded vowels. This conspiracy can be captured by just one universal constraint (*V[-back, +round]) in OT. Therefore, the OT analysis captures greater generality than the rule-based analysis. In order to account for the sound change of /ü:/ and /ü/, we have presented some constraints and their hierarchy.