This paper examines the problem of the selection of first-, second-, and thirddegree undominated portfolios by using the properties of the Laplace transform (L-T) of the distributions of portfolio returns. It is assumed that the joint distribution of n interdependent prospects, as well as its Laplace transform, is known or may be estimated from past data. Next, it is shown that the L-T of the portfolio returns may be expressed very simply in terms of the L-T of the joint distribution. A theorem is then proved, which uses results from L-T theory and shows that stochastic dominance between two portfolios of first-, second- or third-degree may be expressed by inequalities between the L-T's of the portfolios and their derivatives. It is also shown through an example how this theorem may be used in finding undominated portfolios.