Adhesion of biological systems has recently received much research attention: the survival of organisms ranging from single cells and mussels to insects, spiders and geckos relies crucially on their mechanical interaction with their environments. For spiders, lizards and possible other ‘dry’ adhesive systems, explanations for adhesion are based on van der Waals interaction, and the adhesion of single–contact elements has been described by the classical Johnson–Kendall–Roberts (JKR) model derived for spherical contacts. However, real biological contacts display a variety of shapes and only rarely resemble a hemisphere. Here, we theoretically assess the influence of various contact shapes on the pull–off force for single contacts as well as their scaling potential in contact arrays. It is concluded that other shapes, such as a toroidal contact geometry, should lead to better attachment; such geometries are observed in our microscopic investigations of hair–tip shapes in beetles and flies.