Jarzynski's relation between equilibrium free energy and nonequilibrium work is rewritten as an average of work with respect to a work weighted ensemble. The present form is more appropriate for computer application of Jarzynski's relation where the dissipative work is frequently much greater than k(B)T. Monte Carlo sampling of very short nonequilibrium trajectories yields good estimates of the equilibrium free energy change. The procedure can be thought of as a generalization of thermodynamic integration in ordinary free energy calculations. Very short trajectories can be used to compute the free energy difference. In the infinitely short trajectory limit, we recover the thermodynamic integration scheme. We also show that free energy estimate can be obtained from moments of the work distribution. The last result is most useful for experimental measurements of the free energy. (C) 2003 American Institute of Physics.