The finite-time thermodynamic performance has been studied of an endoreversible air heat-pump with constant-temperature heat-reservoirs. The heating load, the coefficient of performance (COP), and the heating-load density, i.e. the ratio of heating load to the maximum specific volume in the cycle, are the optimization objectives. The analytical formulae relating the heating load and pressure-ratio, between the COP and pressure-ratio, as well as between the heating-load density and pressure-ratio are derived assuming heat resistance losses occur in the hot- and cold-side heat-exchangers. The influences of the effectiveness of the heat-exchangers and the heat-reservoir temperature-ratio on the heating load, the COP and the heating-load density are analyzed. The cycle performance optimizations are performed by searching the optimal distribution of heat conductance of the hot- and cold-side heat-exchangers for the fixed total heat-exchanger inventory. The influences of some design parameters, including heat-capacity rate of the working fluid, heat-reservoir temperature-ratio and heat-exchanger inventory on the optimal distribution of heat conductance, the maximum heating load and the maximum heating-load density are indicated by numerical examples. The different results obtained from the heating-load optimization and the heating-load density optimization are shown. The air heat-pump design, with heat-loading density optimization, leads to smaller size equipment. (c) 2007 Elsevier Ltd. All rights reserved.