Orthogonal fluxgates in fundamental mode based on (Co0.94Fe0.06)72.5Si12.5B15 cores have recorded very low noise in literature, especially if Joule annealing is performed on the core for a short period of time. However, for annealing time longer than 20–30 min, the noise of the sensor has a tendency to increase. In this work, we investigated this phenomenon, and we have found its origin in a monotonic increase of magnetostriction during the annealing process. We show that the wires with vanishing magnetostriction in their as-cast form exhibit positive magnetostriction after long-time annealing (more than 30 min), which increases the noise of the sensor. After researching the effect of the magnetostriction after annealing on the noise, we propose an alloy with a reduced amount of iron. Less iron leads to a larger as-cast negative magnetostriction, which becomes almost zero after long-time annealing (60 min), bringing further reduction of noise. We prove this effect on two wires from two different manufacturers, although with the same composition. The noise decrease with prolonged annealing is mainly observable in the low-frequency region: at 100 mHz, the noise of a single-wire sensor decreased from 20pT/Hz to 6pT/Hz when the annealing time was prolonged from 10 to 60 min.