The presence of magnetic noise in magnetoresistive-based magnetic sensors degrades their detection limit at low frequencies. In this paper, different ways of stabilizing the magnetic sensing layer to suppress magnetic noise are investigated by applying a pinning field, either by an external field, internally in the stack, or by shape anisotropy. We show that these three methods are equivalent, could be combined, and that there is a competition between noise suppression and sensitivity reduction, which results in an optimum total pinning field for which the detection limit of the sensor is improved up to a factor of 10. We acknowledge the following organisms for funding: The CEA for the internal funded projects MIMOSA and CALM and the Ph.D. Grant “Phare Amont-Aval,” the Swiss National Science Foundation for a mobility fellowship (Nos. 165238 and 177732) to A. Doll, ANR funding through Grant Nos. ANR-17-CE19-0021-01 (NeuroTMR) and ANR-18-CE42-0001 (CARAMEL). This work was supported by the EMPIR JRP 15SIB06 NanoMag through EU and EMPIR participating countries within EURAMET.