The design optimization of passive vibration control mechanisms in the accelerance domain is discussed. In this study, the fixed points theory is developed which approximately minimizes the maximum accelerance in the frequency domain by equally adjusting the accelerance of two fixed points. This design method is applied to the dynamic vibration absorber (DVA) and the passive gyroscopic damper (PGD), and thus the maximum accelerances of these mechanisms are successfully reduced. The concept of the fixed points theory is reinvestigated. The accuracy and the degree of improvement compared with the fixed points design in the compliance domain are examined. The PGD realizes relatively higher damping effects, and then the accelerance reduction of the PGD by the new design method is considerably larger than that of the DVA with a moderate mass ratio.