Hypothesizing that every syntactic object reaching the interfaces must be labeled, Chomsky (2013Chomsky ( , 2015 introduce an independent label-identifying operation, Labeling Algorithm (LA). This newly proposed LA, which is an instance of Minimal Search, is assumed to search for not only the categorial feature of heads but also any agreeing features shared by two heads to determine the label of a given syntactic object. This paper argues, however, that postulation of the latter type of search by LA (i.e., locating agreeing features) adds a computational burden to the grammar by forcing LA to perform two different types of search, namely, a "comparison search" in addition to the widely agreed-upon Minimal Search. This paper also addresses some conceptual and empirical problems that arise from the paired form of the non-categorial label, <φ, φ>, whose introduction results from the problematic comparison search by LA. To solve these problems, I present an alternative analysis in which LA searches only for the categorial feature of heads. Consequently, neither comparison search nor the paired form of the label, <φ, φ>, becomes necessary in the analysis.