We have investigated the behavior of high-critical-temperature (high Tc) direct-coupled superconducting quantum interference device (SQUID) magnetometers in static and fluctuating magnetic fields. The magnetometers consist of narrow-linewidth superconducting films to prevent flux trap during field cooling. Moreover, they have no superconducting films crossing the bicrystal lines of the substrates (except at the Josephson junctions); i.e., they have no flux dams. When one of these magnetometers was cooled in a static magnetic field Bcool, the low-frequency noise when Bcool<100 μT was as low as that under zero-field cooling, but above 100 μT the noise increased substantially. On the other hand, when a field Bext of less than 4 μT was applied after zero-field cooling, the low-frequency noise increased in proportion to Bext. It returned to its original value reversibly when Bext was turned off. However, when Bext was greater than or equal to 4 μT, the output of the flux-locked-loop started to drift with time and the low-frequency noise increased further. This additional noise increase remained after turning off Bext. These results suggested that there are two modes of increase for the low-frequency noise induced by flux penetration due to the shielding current: a “reversible” mode and an “irreversible” mode. We found that the low-frequency noises of the two modes were additive with respect to their power, suggesting that the two noises derived from independent sources at different sites on the magnetometer. We also found that the reversible-mode noise could be reduced by improving the profile of the film edge.