We make new non-local thermodynamic equilibrium calculations to deduce the abundances of neon from visible-region echelle spectra of selected Ne i lines in seven normal stars and 20 HgMn stars. We find that the best strong blend-free Ne line that can be used at the lower end of the effective temperature Teff range is λ6402, although several other potentially useful Ne i lines are found in the red region of the spectra of these stars. The mean neon abundance in the normal stars (log A=8.10) is in excellent agreement with the standard abundance of neon (8.08). However, in HgMn stars neon is almost universally underabundant, ranging from marginal deficits of 0.1–0.3 dex to underabundances of an order of magnitude or more. In many cases, the lines are so weak that only upper limits can be established. The most extreme example found is υ Her with an underabundance of at least 1.5 dex. These underabundances are qualitatively expected from radiative acceleration calculations, which show that Ne has a very small radiative acceleration in the photosphere, and that it is expected to undergo gravitational settling if the mixing processes are sufficiently weak and there is no strong stellar wind. According to theoretical predictions, the low Ne abundances place an important constraint on the intensity of such stellar winds, which must be less than 10−14 M⊙ yr−1 if they are non-turbulent
