Alfvén waves and ion-cyclotron absorption of high-frequency waves are frequently brought into models devoted to coronal heating and fast solar-wind acceleration. Signatures of ion-cyclotron resonance have already been observed in situ in the solar wind and in the upper corona. In the lower corona, one can use the line profiles to infer the ion temperatures. But the value of the so-called "non-thermal" (or "unresolved") velocity, potentially related to the amplitude of Alfvén waves propagating in the corona, is critical in firmly identifying ion-cyclotron preferential heating. In a previous paper, we proposed a method to constrain both the Alfvén wave amplitude and the preferential heating, above a polar coronal hole observed with the SUMER/SOHO spectrometer. Taking into account the effect of instrumental stray light before analysing the line profiles, we ruled out any direct evidence of damping of the Alfvén waves and showed that ions with the lowest charge-to-mass ratios were preferentially heated. We re-analyse these data here to correct the derived non-thermal velocity, and we discuss the consequences on the main results. We also include a measure of the Fe VIII 1442.56 Å line width (second order), thus extending the charge-to-mass ratio domain towards ions more likely to experience cyclotron resonance.