An adaptive Exponential Integrate-and-Fire (aEIF) model was used to predict the activity of layer-V-pyramidal neurons of rat neocortex under random current injection. A new protocol has been developed to extract the parameters of the aEIF model using an optimal filtering technique combined with a black-box numerical optimization. We found that the aEIF model is able to accurately predict both subthreshold fluctuations and the exact timing of spikes, reasonably close to the limits imposed by the intrinsic reliability of pyramidal neurons.