Vibration isolation systems are widely used in engineering practice in order to reduce the transmission of the unwanted vibrations from the foundation to equipment. In last decades for this purpose commonly are considered nonlinear vibration isolators (NVIs), which usually are much more effective than linear ones. At the same time, the comprehensive analysis of the dynamics of the NVI is rather difficult, because even for a single Degree-of-Freedom (sDOF) system there is a multiparameter problem, and conventional grid search in parameter space may be computationally costly. This leads to the need for a preliminary analytical study of the model in order to identify “favorable” regions in the parameter space to reduce displacement and/or force transmissibility of an isolator. In present study we consider sDOF isolators with nonlinear stiffness and damping. Assuming that amplitude and frequency of external excitation are unknown we suggest a procedure to determine the stiffness and damping values (or, to put it more precisely, ratios between linear and nonlinear components) which allow satisfactory reduction of the transmissibility for a given range of frequency values. In particular, the case study of quasi-zero stiffness NVI is analyzed, and results are compared with those known from the literature.