When verifying the validity of the exponential-decay law through 137 precise decay rate measurement series at various nuclear laboratories, minor violations have been observed in the shape of annual cycles in the residuals with different amplitudes and phase shifts. The timing and amplitude of these deviations have been compared with local weather data and it appears that ambient humidity is highly correlated with the observed instabilities in these radioactivity measurements. In fact, when compensating the residuals for a linear relationship with absolute humidity in air, most of the annual cycles are no longer statistically significant. As a result, the validity of the exponential-decay law can now be demonstrated with even higher fidelity.