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Ion beam analysis (IBA) is a powerful materials characterization technique with verywide applicability. However, despite the fact that most natural and many industrial samples are rough, there is currently no way to correctly take severe roughness into account when processing the IBA spectra from rough samples, without resorting to Monte Carlo calculations which are too slow for routine use. In the present work we demonstrate a new approach which parameterises a Monte Carlo calculation so that the analytical codes can rapidly calculate the effect of asperities for a wide variety of rough surfaces. We successfully apply this method to real samples. This new analytical algorithm allows us to overcome the long standing problem of the correct depth profiling of these common samples, hence dramatically increasing the power of the IBA technique. It also allows us to extract physically meaningful roughness parameters on samples whose roughness cannot be easily measured directly.