Dependency length minimization (DLM) is a well-documented processing universal, but previous studies report a single mean dependency distance (MDD) per language, obscuring variation across syntactic relation types. We analyze 122 languages in UD and SUD (version 2.17), showing that DLM operates on two distinct levels. Grammar-driven optimization targets functional dependencies (det, case, aux), which are universally short (mean 1.71, $σ$ = 0.33) and invariant across typologically diverse languages. Processing-driven optimization operates on lexical dependencies (nsubj, obj, obl), which are longer (mean 2.87), highly variable ($σ$ = 0.63), and constrained by word-order typology. This asymmetry holds in SUD despite reversed head direction (r = 0.92). We conclude that ''the grammar does the work'' of minimization by scaffolding sentences with local functional attachments, leaving processing pressures to determine the ordering of lexical heads.

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