Subsumption is an important redundancy elimination method in automated deduction. A clause D is subsumed by a set C\mathcal{C} of clauses if there is a clause C C\mathcal{C} and a substitution C\mathcal{C} to a set of atoms. Both clausal and atomic H-subsumption play an indispensable key role in automated model building. Moreover, problems equivalent to atomic H-subsumption have been studied with different terminologies in many areas of computer science. Both clausal and atomic H-subsumption are known to be intractable, i.e., _p ² -complete and NP-complete, respectively. In this paper, we present a new approach to deciding (clausal and atomic) H-subsumption that is based on a reduction to QSAT₂ and SAT, respectively.