Data are presented for 17 separate occurrences of Kelvin-Helmholtz billows in the upper troposphere for which the crest-to-trough amplitude exceeded 200 m. The billows were detected in clear air by means of high-power radar. The associated mesoscale patterns of static stability, vertical wind shear, and Richardson number have been derived from sequences of hourly radiosondes tracked by precision radar. Every occurrence of billows was found to be closely associated with well-defined, local, wind-shear maxima. In some cases the shear was as strong as 9 m s−1 per 200 m. The minimum value of the Richardson number when evaluated over layers 200 m deep was usually found to be in the range 0.15–0.3.