In a mixed-layer surface duct, acoustic transmission at frequencies below that required for duct trapping, as well as at frequencies moderately higher, is subject to coherent leakage of energy to the thermocline. The rate of coherent leakage with range is related to the imaginary part of the horizontal wavenumber of a mode, for which an iterative technique is commonly used for evaluations. In order to obtain alternative direct analytic expressions of the leakage rate, the analysis of Furry, described, for example, by Pederson and Gordon (JASA 47, 304–326, 1970), has been revisited. Consideration has been given to both very large and very small ratios between sound speed gradients in the duct and below the duct, and ratios of sound speed gradients typical of those encountered as sea. The leakage rate for the first mode was found to well approximate the total signal leakage, hence the proposed analytical expressions relate to the first mode. Leakage values based on these expressions are compared against results from both a modal model and a wavenumber integration model, and a pre-existing approximate expression for leakage, for a number of surface ducted scenarios for frequencies relevant to the onset of duct trapping.