This paper discusses why the ellipsis of the complement of a Preposition(P) cannot be allowed in the general case. In principle this is unexpected if we consider that P is a functional category which is also eligible to be a licensing head of ellipsis, along with other functional categories such as T, C, and D, all of which can be the licensor of ellipsis in a variety of elliptical constructions. In this paper, I argue that the reason why a functional category P cannot allow ellipsis of its complement may be attributable to a PF-constraint; the so-called “Stranded Affix Filter(SAF)”(Lasnik 1981), in conjunction with the (a)tonicity of P(Gallego 2009, 2011). Concretely, I suggest that if P is atonic and thus cannot stand alone at PF, the complement of P cannot be elided due to the SAF imposed on P, whereas if P is tonic and can thus stand alone at PF, it is not subject to the SAF and thereby can be survived at PF after the deletion of its complement. To explore more of the possibility of ellipsis in the prepositional domain, I also discuss issues related to the ellipsis of PP as well as other instances where the complement of P is missing on the surface.