This paper addresses the question to what extent parallel-plate heat exchangers can be downsized 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. The point of maximal effectiveness is found to correspond to a maximal thermal power density and thus to the minimal volume required for obtaining that effectiveness. Based on asymptotic relations for the effectiveness in the small and large channel limit, closed-form expressions are derived for the optimum geometric parameters that maximize power density in the limit of design effectiveness approaching unity. These relations are extended to a broader effectiveness range by means of dimensionless correction functions that are calculated numerically. The resulting expressions define optimal elemental units that can be used to construct parallel-plate counter-flow heat exchangers with the lowest possible core volume for effectiveness values between 0.53 and 1. (C) 2009 Elsevier Ltd. All rights reserved.