A shallow (depth < 20 m) layer of water, fresh, brackish or saline, covers millions of square kilometres of sediments and bedrock along the world's coastlines, rivers, lakes, and lagoons. These geological units are extremely important, both environmentally and economically. Airborne electromagnetic (AEM) has been used with some success to obtain the bathymetry of shallow surface water ((Macnae et al., 2004; Vrbancich et ah, 2000; Vrbancich et ah, 2005). Some attempts have also been made to retrieve information about the sediments under the water bottom (Vrbancich et ah, 2000). The limited research that has been carried out so far tells us that we need to make improvements and further developments, both in hardware, as well as in data processing and modelling. This manuscript aims at making a contribution at the data inversion level, by applying constrained inversion methodology to different AEM datasets flown over water. In constrained inversion, adjacent model parameters are regularized through lateral constraints that allow information to flow from soundings that contain more information to those that contain less. We present results from constrained inversion (smooth and few layers) of a portion of SkyTEM survey (a helicopter borne time domain AEM system) flown in Denmark, and of a RESOLVE survey (a helicopter borne frequency domain AEM system) carried out along the Murray River in Australia. In both cases bird height was included as an inversion parameter, allowing the inversion to compensate for errors in laser altimeter readings over water.