Space-based nulling interferometers will play a major role in the search for exoplanets, as both NASA and ESA plan missions for the near future. Current architectures produce the requisite broadband π phase shift in one arm of each nulling telescope pair by means of a system of "field flip" optics that may involve one of a number of sophisticated technologies (periscope, phase plates, through-focus, or other). The two beams, of equal intensity but conjugate phase, are then combined, perhaps in a modified Mach-Zehnder (MMZ) or similar beam combiner of high configurational symmetry. A novel approach has recently been proposed, however, in which the achromatic π phase shift is supplied by two applications of the innate π/2 phase shift between transmitted and reflected beams in a beam splitter. This simply requires using the traditionally bright output port of the MMZ as a nulled port; adaptive nulling can be used to ease the tolerances on matching the moduli of reflection and transmission coefficients. The rather substantial systems benefit that accrues is that the external phase shifting ("field flipping") optics may be entirely eliminated. Here, I discuss the feasibility of this "self-nulling" beam combiner scheme.