A fundamental function of any portfolio selection model is the identification of inefficient portfolios and the consequent reduction of the set of alternative investments that the decision maker must evaluate. In the absence of a specific utility function, the establishment of criteria for the identification of inefficient portfolios must strike a compromise in terms of convenience and effectiveness. Of the myriad possibilities, models employing a criterion based on two parameters have been found most convenient for reasons of simplicity of interpretation and computational feasibility. Certainly, the most popular of the two parameter models has been the expected value-variance (E-V) formulation first proposed by Markowitz [7]. The basic E-V model developed for individual decision making has been extended by Sharpe, Lintner, and others [1, 4, 3, 9] to set forth an extensive theory which seeks to explain the equilibrium price of risky assets. The purpose of the present paper is to review and extend some of the implications of an alternative two-parameter portfolio selection model, called the expected value-semivariance model (E-S). In particular, the discussion focuses on certain contrasts and similarities between the E-V and the E-S models.