We examine the influence of activity- and telluric-induced radial velocity signals on high resolution spectra taken with an iodine absorption cell. We exclude 2 Angstrom spectral chunks containing active and telluric lines based on the well characterised K1V star Alpha Centauri B and illustrate the method on Epsilon Eridani - an active K2V star with a long period low amplitude planetary signal. After removal of the activity- and telluric-sensitive parts of the spectrum from the radial velocity calculation, the significance of the planetary signal is increased and the stellar rotation signal disappears. In order to assess the robustness of the procedure, we perform Monte Carlo simulations based on removing random chunks of the spectrum. Simulations confirm that the removal of lines impacted by activity and tellurics provides a method for checking the robustness of a given Keplerian signal. We also test the approach on HD 40979 which is an active F8V star with a large amplitude planetary signal. Our Monte Carlo simulations reveal that the significance of the Keplerian signal in the F star is much more sensitive to wavelength. Unlike the K star the removal of active lines from the F star greatly reduces the radial velocity precision. In this case, our removal of a K star active lines from an F star does not a provide a simple useful diagnostic because it has far less radial velocity information and heavily relies on the strong active lines.