Searches for gravitational waves crucially depend on exact signal processing of noisy strain data from gravitational wave detectors, which are known to exhibit significant non-Gaussian behavior. In this paper, we study two distinct non-Gaussian effects in the LIGO/Virgo data which reduce the sensitivity of searches: first, variations in the noise power spectral density (PSD) on timescales of more than a few seconds; and second, loud and abrupt transient `glitches of terrestrial or instrumental origin. We derive a simple procedure to correct, at first order, the effect of the variation in the PSD on the search background. Given the knowledge of the existence of localized glitches in particular segments of data, we also develop a method to insulate statistical inference from these glitches, so as to cleanly excise them without affecting the search background in neighboring seconds. We show the importance of applying these methods on the publicly available LIGO data, and measure an increase in the detection volume of at least $15%$ from the PSD-drift correction alone, due to the improved background distribution.
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