Towing-tank experiments on linearly stratified flow over three-dimensional obstacles of various shapes are described. Particular emphasis is given to the parameter regimes which lead to wave-breaking aloft, the most important of which is the Froude number, the Brunt-Vaisala frequency and the hill height, respectively. The effects of other parameters and the spanwise and longitudinal aspect ratios of the hill, on wave breaking are also demonstrated. It is shown that the Froude number range over which wave breaking occurs is generally much more restricted than the predictions of linear (hydrostatic) theories would suggest; nonlinear (Long's model) theories are in somewhat closer agreement with experiments. The results also show that a breaking wave aloft can exist separately from a further recirculating region downstream of the hill under a second lee wave, but that under certain circumstances these can interact to form a massive turbulent zone whose height is much greater than h. Previous theories only give estimates for the upper critical Froude number, below which breaking occurs; the experiments also reveal lower critical values, below which there is no wave breaking.