It is well known that for a thermoelectric generator (TEG) in thermal steady-state with constant temperature difference across it the maximum power point is found at half of the open-circuit voltage (or half of the short-circuit current). However, the effective thermal resistance of the TEG changes depending on the current drawn by the load in accordance with the parasitic Peltier effect. This article analyses the different case in which the input thermal power is constant and the temperature difference across the TEG varies depending on its effective thermal resistance. This situation occurs in most waste heat recovery applications because the available thermal power is at any time limited. The first part of this article presents the electrical characterisation of TEGs for constant-heat and it investigates the relationship between maximum power point and open-circuit voltage. The second part studies the maximum power that can be produced by TEGs with pellets (or legs) of different size and number, i.e. with different packing factors, and of different height. This work provides advice on the optimisation of the pellets geometrical parameters in order to increase the power generated, and consequently the thermodynamic efficiency, and to minimise the quantity of thermoelectric material used, for systems with limited input thermal power. (C) 2015 The Authors. Published by Elsevier Ltd.