A novel method is presented for measuring the spectral density of resistance fluctuations without the explicit determination of the voltage background noise (Johnson noise, pre-amplifier noise). The output of a standard ac bridge excited by a single-frequency alternating current is demodulated by two phase-sensitive detectors which operate in quadrature. When the phase difference between excitation and detection is properly set, the real part of the cross-spectral density of the two demodulators shows only the spectral density of the resistance fluctuations and not the disturbing background noise. The feasibility of our new method is demonstrated by measurements of 1/f noise of a thin-film A1 sample. © 1989 Springer-Verlag.