1. Orientation with respect to the sun has been observed in a wide range of species and has generally been interpreted in terms of thermoregulation and/or ultraviolet (UV) protection. For countershaded animals, orientation with respect to the sun may also result from the pressure to exploit the gradient of coloration optimally to enhance crypsis. 2. Here, we use computational modelling to predict the optimal countershading pattern for an oriented body. We assess how camouflage performance declines as orientation varies using a computational model that incorporates realistic lighting environments. 3. Once an optimal countershading pattern for crypsis has been chosen, we determine separately how UV protection/irradiation and solar thermal inflow fluctuate with orientation. 4. We show that body orientations that could optimally use countershading to enhance crypsis are very similar to those that allow optimal solar heat inflow and UV protection. 5. Our findings suggest that crypsis has been overlooked as a selective pressure on orientation and that new experiments should be designed to tease apart the respective roles of these different selective pressures. We propose potential experiments that could achieve this.