A strong claim about human sentence comprehension is that the processing mechanism is fully innate and applies differently to different languages only to the extent that their grammars differ. If so, there is hope for an explanatory project which attributes all parsing “strategies” to fundamental design characteristics of the parsing device. However, the whole explanatory program is in peril because of the discovery (Cuetos & Mitchell, 1988) that Late Closure is not universal: Spanish, and also Dutch and other languages, favor Early Closure (high attachment) where English favors Late Closure flow attachment). I argue that the universal parser can weather this storm. Exceptions to Late Closure in Spanish and other languages are observed only in one construction (a relative clause attaching into a complex noun phrase [NP]), which is borderline in English too. For other constructions, low attachment is preferred in all languages tested. I propose that what differentiates the complex NP construction is the heaviness of the attachee compared to that of the host configuration. A relative clause is a heavy attachee, and the lower NP alone is small as a host; the relative is therefore better balanced if the whole complex NP is its host. A wide range of facts is accounted for by the principle that a constituent likes to have a sister of its own size. Light constituents will tend to attach low, and heavy ones to attach high, since larger constituents are dominated by higher nodes. A preference for balanced weight is familiar from work on prosodic phrasing. I suggest, therefore, that prosodic processing occurs in parallel with syntactic processing (even in reading) and influences structural ambiguity resolution. Height of attachment ambiguities are resolved by the prosodically motivated same-size-sister constraint. The exceptional behavior of English may be due to its prosodic packaging of a relative pronoun with the adjacent noun, overriding the balance tendency. If this explanation is correct, it is possible that all cross-language variations in parsing preferences are due to cross-language variations in the prosodic component of the competence grammar.