The paper presents a new approach to the minimisation of line losses in a given power-system network by means of certain sensitivity coefficients. These coefficients are used to see how sensitive is the line loss for small changes in the control variables, i.e. voltage magnitudes of the generators, reactive-power injections by VAR sources and transformer tap ratios. These sensitivity coefficients are derived using an eigenvector of the transposed Jacobian matrix. After establishing the objective function for minimising the system losses with the help of linearised sensitivity relationships of control variables, a dual linear programming (LP) technique is used to determine the optimum adjustments to the control variables, simultaneoulsy satisfying the constraints like reactive-power limits of the generators, limits on the load busbar voltages and the operating limits of the control variables.