We study the shape optimization problem where the objective function is a convex combination of three sequential Laplace-Dirichlet eigenvalues. That is, for alpha a parts per thousand yen0, beta a parts per thousand yen0, and alpha+beta a parts per thousand currency sign1, we consider . Here lambda (k) (Omega) denotes the k-th Laplace-Dirichlet eigenvalue and |a <...| denotes the Lebesgue measure. For k=1,2, the minimal values and minimizers are computed explicitly when the set of admissible domains is restricted to the disjoint union of balls. For star-shaped domains, we show that for k=1 and alpha+2 beta a parts per thousand currency sign1, the ball is a local minimum. For k=1,2, several properties of minimizers are studied computationally, including uniqueness, connectivity, symmetry, and eigenvalue multiplicity.