We present results of density-functional calculations on the magnetic properties of Cr, Mn, Fe and Co nanoclusters (1-9 atoms large) supported on Cu(001) and Cu(111). The inter-atomic exchange coupling is found to depend on competing mechanisms, namely ferromagnetic double exchange and antiferromagnetic kinetic exchange. Hybridization-induced broadening of the resonances is shown to be important for the coupling strength. The cluster shape is found to affect the coupling via a mechanism that comprises the different orientation of the atomic d-orbitals and the strength of nearest-neighbour hopping. Especially in Fe clusters, a correlation of binding energy and exchange coupling is also revealed. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim