Properties of the conductance and transport channels of atomic-scale contacts are discussed within the free electron model. In agreement with recent experiments, we find that, owing to the contribution of evanescent channels, even when the conductance is close to an integer number N of conductance quanta more than N channels may contribute significantly to the current. We show that the observation of peaks at integer multiples of G 0 in conductance histograms is not a signature of conductance quantization of individual contacts. However, the observed peaks can still be associated to the quantum nature of electron transport in metallic contacts. DGCyT PB95-0061 DGCyT FPI Grant IN92-D00830413