A method for the detection, qualification, and quantification of nonlinear distortions on a frequency response function (FRF) measurement was described in previous papers by Schoukens et al.. The kernel idea of that method is to use well-chosen periodic excitations where only some of the considered frequency components are excited. The nonexcited frequency lines (detection lines) are used to detect, qualify, and quantify the nonlinear distortions. Due to the presence of a low-quality generator, a nonlinear actuator, or due to the interaction of the generator with the nonlinear system, unwanted excitation power can be present at the detection lines at the input of the system. In this case, the basic conditions necessary to apply the detection method are no longer valid. In this paper, a first-order compensation method is described that allows the detection, qualification, and quantification of nonlinear distortions on the FRF measurement with the original technique of previous papers by Schoukens et al., in the case that the desired input cannot be applied at the device under test. This first-order compensation method is illustrated on simulations and a real measurement example.