Supersymmetry confers many nice properties on a theory, including the existence of BPS solutions that may be easier to construct than more general non-supersymmetric ones; positivity properties for the energy; stability arguments, and so on. For many of these purposes, it is not in fact necessary to make use of the full edifice of the exact supersymmetry of the theory; for the purposes of studying bosonic solutions, most of the information, such as the supersymmetry of the background, can be extracted merely from the knowledge of the supersymmetry at the quadratic order in fermions. Here, we report on a recent construction of a "pseudo-supersymmetric" extension of the effective action of the bosonic string in arbitrary spacetime dimension D. This theory is invariant under pseudo-supersymmetry transformations up to the quadratic fermion order. Further extensions including a Yang-Mills pseudo-supermultiplet, and the addition of alpha' corrections, are also discussed.