We introduce a new variable selection method, suitable when the correlation between regressors is known. It is appropriate in genomics since once the genetic map has been built, the correlation is perfectly known. Our method, based on the LASSO , is original since the number of selected variables is bounded by the number of predictors, instead of being bounded by the number of observations as in the classical LASSO. It is made possible by the construction of a specific statistical test, a transformation of the data and by the knowledge of the correlation between regressors. We prove that the signal to noise ratio is largely increased by considering the extremes. This new technique is inspired by stochastic processes arising from statistical genetics. It is described in a statistical genetics context, considering a large panel of models present in the literature. Our method is insensitive to interactions between regressors. An illustration on simulated data is given.