Abstract When bright solar-system objects are observed by GHz-THz regime telescopes, off-axis signals bounce around locally and re-enter the signal path with a time delay, causing sinusoidal ripples in output spectra. Ripples that are unstable over time are challenging to remove. A typical detection limit for planetary spectral lines is a fraction ∼10−3 of continuum signal, restricting searches for minor atmospheric trace-gases. Modern wideband spectra of Venus demonstrate a plethora of effects, at three example telescopes spanning nearly a factor-of-50 in frequency. Characterisation of instrumental effects as families of pure sine-waves via Fourier-analysis is shown to improve dynamic-range by factors of a few. An example upper limit on sulphuric acid (H2SO4) vapour in Venus’ mesosphere, from fully-automated data-cleaning of a 3.5 GHz band containing 10 line components, goes as deep as the best previously-published limit. The most challenging cases are searches for single lines of width comparable to ripple periods. Traditional polynomial-fitting approaches can be deployed to test for false positives, to demonstrate robustness at a level of zero ”fake lines” in >1000 comparisons. Fourier-based data-cleaning avoids subjectivity and can be fully automated, and synthetic spectra can be injected before processing to test to what degree signals are lost in cleaning. An ideal robustness strategy is mitigation at the data-acquisition stage, e.g. using slow drifts in target-velocity with respect to the telescope to isolate a planetary line from a quasi-static instrumental ripple pattern.