This paper addresses the question to what extent parallel-plate cross-flow heat exchangers can be down-sized without loss of thermal-hydraulic performance. It is shown that when the characteristic length scales of the channels are reduced at a constant pressure drop, the effectiveness exhibits a maximum due to axial heat conduction in the plate material. The point of maximal effectiveness is found to correspond to a maximal thermal power density and thus to the minimal volume required for obtaining a given effectiveness. From an asymptotic analysis, closed-form expressions are derived for the optimal geometric parameters that maximize power density. The resulting expressions define optimal elemental units that allow constructing parallel-plate cross-flow heat exchangers with the lowest possible core volume for effectiveness values between 0.55 and 1. (C) 2013 Elsevier Ltd. All rights reserved.