This paper deals with the optimization of the "spinning-current" modulation method for cancelling the lowfrequency noise at the output of a Hall sensor. This method, based on Onsager reciprocity relationships through the reversemagnetic-field-reciprocity theorem of Sample et al., allows extracting magnetic field signals whose spectral intensity is much lower than the PSD of the low-frequency (LF) noise observed in the measurement: this includes the LF noise of the Hall sensor, the LF noise of the preamplifier, or the environmental noise due to electromagnetic interferences (EMI). Contrarily to methods based on the lock-in detection principle, which results in a narrow bandpass filtering, the LF-noise-free magnetic sensor signal remains broadband (DC to kHz). An improvement of 30dB in the S/N ratio can be observed around 1 Hz.