The evolution of the structure and conductance of an Al nanowire subject to a tensile stress has been studied by first-principles total-energy simulations. Our calculations show the correlation between discontinuous changes in the force (associated to changes in the bonding structure of the nanowire) and abrupt modifications of the conductance as the nanowire develops a thinner neck, in agreement with the experiments. We reproduce the characteristic increase of the conductance in the last plateau, reaching a value close to the conductance quantum $G_0 = 2 e^2 / h$ before the breaking of the nanowire. A dimer defines the contact geometry at these last stages, with three channels (one dominant) contributing to the conductance. Comment: 4 pages, 4 figures