Cubic perovskite compounds of the form (A(1/3)A(')(1/3)A(")(1/3))BO3 and A(B(1/3)B(')(1/3)B(")(1/3))O3, in which the differentiated cations form an alternating series of monolayers, are studied using first-principles methods. Such compounds are representative of a possible new class of materials in which ferroelectricity is perturbed by compositional breaking of inversion symmetry. For isovalent substitution the ferroelectric double-well potential becomes asymmetric, so that minority domains may no longer survive. The symmetry breaking is enormously stronger for heterovalent substitution; here the double-well behavior is destroyed. Tuning between these behaviors may allow for the optimization of desired materials properties.