Highly overventilated laminar coflow diffusion flames in axisymmetric geometry are addressed for Lewis numbers of unity in the reaction-sheet approximation with effects of buoyancy taken into account. A simple method of numerical integration with the boundary-layer approximation in stream-function coordinates is given, and results for flame structures and for Lagrangian histories are presented for hydrocarbon-air flames. Computed flame heights are shown to be in good agreement with experiment. The computational approach can efficiently employ standard routines on low-power work stations and personal computers.