Gradient coil windings are typically constructed from either variable width copper tracks or fixed width wires. Excessive power dissipation within these windings during gradient coil operation limits the maximum drive current or duty cycle of the coil. It is common to design gradient coils in terms of a continuous minimum power current density and to perform a discretization to obtain the locations of the coil tracks or wires. However, the existence of finite gaps between these conductors and a maximum conductor width leads to an underestimation of coil resistance when calculated using the continuous current density. Put equivalently, the actual current density within the tracks or wires is higher than that used in the optimization and this departure results in suboptimal coil designs. In this work, a mapping to an effective current density is proposed to account for these effects and provide the correct contribution to the power dissipation. This enables the design of gradient coils that are genuinely optimal in terms of power minimization, post-discretization. The method was applied to the theoretical design of a variety of small x- and z-gradient coils for use in small animal imaging and coils for human head imaging. Computer-driven comparisons were made between coils designed with and without the current density mapping, in terms of simulated power dissipation. For coils to be built using variable width tracks, the method provides slight reductions in power dissipation in most cases and substantial gains only in cases where the minimum separation between track centre-lines is less than twice the gap size. However, for coils to be built using fixed width wires, very considerable reductions in dissipated power are consistently attainable (up to 60%) when compared to standard approaches of coil optimization.