We introduce a generalization of the computational model of S-machines and explore how it is employed to obtain the following refinement of Higman's embedding theorem: Every finitely generated recursively presented group may be embedded as a malnormal subgroup of a finitely presented group. The properties of this embedding are then examined; for example, that the embedding is a quasi-isometry, producing a refinement of several theorems of Olshanskii. Finally, we discuss how the embedding may be constructed to preserve the decidability of the word problem, yielding a refinement of a theorem of Clapham.