Applications of market share models which (implicitly) rely on Luce's choice axiom have been widely criticized because they cannot account for the effects of differential product substitutability and product dominance. Three types of choice models—Tversky's Elimination-By-Aspects model, Tree Models, and Generalized PROBIT—have been offered as solutions to the problems identified with the Luce model, but they each suffer from limitations which have prevented their widespread application in marketing contexts. Tversky's elegant EBA model has not been widely used because it requires a large number of parameters and no special-purpose parameter estimation software has yet emerged. Tree models have been offered as more parsimonious special cases of EBA, but they are more restrictive in that they presume: (1) that products, and the process of choosing from among them, can be characterized in terms of hierarchical, attribute-based trees; and (2) that the aspects governing choice are well-known. Generalized PROBIT can paramorphically handle the problems with the Luce model, but parameter estimation software has proved problematic because it cannot guarantee a globally optimum solution. This paper proposes a new class of market share models. Rather than model the choice process explicitly, the new models simply scale the effects competing products have on each other's market share. These competitive effects are scaled in the context of a class of market-share models which: (1) do not assume a tree-like structure for the competing products; (2) do not presume any a priori knowledge about the attributes governing choice; (3) are characterized in terms of parameters that can be estimated using ordinary least-squares; and (4) provide clear managerial insight into the sources of competition. The paper begins with a brief review of previous work. Following the review, the paper offers a theorem and proof which guarantees the existence of the new class of models. The empirical validity and strategic utility of the models are demonstrated using two separate sets of data.