Multiple reflections in large radiotelescopes used for astronomical spectroscopy cause characteristic modulations of the observed spectrum (“baseline ripple”). For a given mechanism, the magnitude of the effect depends primarily on the reflection coefficient, which for the most important paths is proportional to λ. Although ripple is thus generally negligible at mm-wavelengths, there are some instances where it may still be significant, and a recent experiment at the15 m James Clerk Maxwell Telescope was severely affected. We describe a technique which has proved effective in reducing the ripple to an acceptable level. The purpose of this research note is to draw this technique to the attention of the astronomical community. We calculate the reflection coefficient for a typical instrument and show that it can be greatly reduced over a very broad bandwidth by means of a tapered absorber in the centre of the secondary mirror. The graphical analysis of the tapered absorber also demonstrates that the scattering cones and circular absorbers widely used in radioastronomy donot in fact reduce the reflection coefficient significantly.