If a constituent C has the potential for a type of movement M, a structurally lower constituent cannot undergo M across C in certain contexts, as reported in Li, Shields and Lin (2012). Neither the Relativized Minimality Condition nor the Minimal Link Condition alone can account for this new fact. It is argued that an empirically adequate model of UG may keep the MLC but must also include two more mechanisms. Ternary-valued features accommodate potential movability. The Feature Value Assignment Protocol relies on computational cost to regulate how the inherent values of any given feature are actually represented in syntactic operations. While this theory offers a unified account of all known facts of minimality (wh-island, potentiality-related movements of adverbs, superiority, super-raising, local and long head movements), it also bears on more fundamental concerns of theoretical simplicity and data idealization. It is argued with both linguistic cases like minimality and the previously axiomatic notion of government and cases of physics (friction, Maxwell’s equations) that the understanding of simplicity often found in syntactic theorization is overly simplistic.