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We present and discuss new importance sampling schemes for the approximatecomputation of the sample probability of observed genetic types in theinfinitely many sites model from population genetics. More specifically, weextend the 'classical framework', where genealogies are assumed to be governedby Kingman's coalescent, to the more general class of Lambda-coalescents anddevelop further Hobolth et. al.'s (2008) idea of deriving importance samplingschemes based on 'compressed genetrees'. The resulting schemes extend earlierwork by Griffiths and Tavar\'e (1994), Stephens and Donnelly (2000), Birknerand Blath (2008) and Hobolth et. al. (2008). We conclude with a performancecomparison of classical and new schemes for Beta- and Kingman coalescents.

Importance sampling for Lambda-coalescents in the infinitely many sites model