Secondary gravity waves excited in the middle atmosphere contribute to vertical coupling and are not well understood. Using a novel analysis method based on two-dimensional wavelet analysis, we select gravity waves depending on their apparent vertical phase velocity using lidar temperature soundings in the 30 to 85 km altitude range. Wave packets of upward and downward-propagating gravity waves can thus be separated and quantified. From two Rayleigh lidar datasets obtained in Finland and New Zealand, we present cases with enhanced occurrence of downward-propagating waves and study possible wave generation mechanisms.