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General directions for rough optimal calibration of Stirling machines can be given by a non-dimensional Schmidt model (nDSM). Since different relative parameters and performance indices have been analyzed by nDSM models, there is lack of uniform conclusions in the literature. This paper describes a new nDSM of six parameters and compares four performance indices as functions of relative parameters. Two optimization tasks of two and five parameters are formulated and solved using the nDSM. Maximized criterion is cycle work per unit of mean pressure and total swept volume. An optimization code based on the algorithm of conjugate gradients with projection on linear constraints is described. The optimal values of volume phase angle, nondimensional swept volume, and dead volume are presented for different constraints imposed on temperature ratio and relative dead volumes.