Point-absorbing wave energy converters (WECs) with a single-tether mooring are capable of extracting power from heave motion, but they do not utilise the full energy harvesting potential. One of the possible ways to increase the total power absorption is to add another controllable degree of freedom. These can be achieved by using a so-called ‘tripod’ configuration when the body is tied to three tethers attached to the power take-off systems at the sea floor. This paper investigates the optimal inclination of tethers considering two different approaches: a purely kinematic analysis, not taking into account the shape of the buoy and a dynamic analysis of spherical and cylindrical WECs, using a linear frequency-domain method. The results show that for a submerged sphere and for a submerged vertical cylinder with an aspect ratio of one, tethers should be orthogonal to each other, forming edges of the cuboidal vertex. Such a configuration of tethers provides for uniform performance of the WEC in all directions of motion. However, for the cylinders with an aspect ratio other than one, an optimal angle between the tethers depends greatly on the ratio between the cylinder height and diameter.