In this paper, we assume Chomsky's (2005, 2007, 2008) feature inheritance framework as an attempt to explain the correlation between the presence of C and agreement/finiteness on T in English. We argue, however, against one of its critical assumptions, namely, that T is a head deprived of φ-features (i.e., a mere feature receptacle as put by Richards 2007). The proposal of this paper is three-fold. First, based on the possibility of ellipsis in different infinitival contexts, we argue that there are two types of T heads in English: the one used in ECM contexts, containing no φ-features, and the other occurring in finite/control/raising clauses and for-infinitives, which contains (at least) a person feature. Second, even though finite clauses, for-infinitives, and control clauses are all headed by C, only the T head in finite clauses displays full agreement. We show that maintaining the feature inheritance hypothesis in the face of this challenge leads us to further distinguish two types of C heads in English: only the C head in for-infinitives is φ-complete, whereas that in finite/control clauses hosts only an inherent number feature. Finally, after reviewing the problems with existing motivations for Chomsky's feature inheritance hypothesis, we advance a novel approach to feature inheritance in which only the number feature is inherited as a last resort strategy to form a φ-complete head for Case valuation in a phase.