A shallow (depth < 20 m) layer of water, fresh, brackish or saline, covers of millions of km2of sediments and bedrock along the world's coastlines, rivers, lakes, and lagoons. Thesegeological units are extremely important, both environmentally and economically. Airborneelectromagnetic (AEM) data has been used with some success to obtain the bathymetry ofshallow surface water ((Macnae et al., 2004; Vrbancich et al., 2000; Vrbancich et al., 2005).Some attempts have also been made to retrieve information about the sub-bottom(Vrbancich et al., 2000 ). The limited research carried out so far calls for improvements andfurther developments, both hardware and in data processing and modelling. This manuscriptaims at giving a contribution at data inversion level, by applying the constrained inversionmethodology to different AEM datasets flown over water. In this technique, adjacent modelparameters are regularized through lateral constraints that allow information to flow fromsoundings that contain more to those that contain less. We present results from constrainedinversion (smooth and few layers) of a portion of SkyTEM (TEM system) survey flown inDenmark, and of a RESOLVE (HEM system) survey carried out along the Murray river inAustralia. In both cases bird height was included as an inversion parameter, allowingcompensating for errors in laser altimeter reading over water.