Situations of correlated and linearly dependent variables often exist in genomic datasets and lead to under-performance of classical methods of variable selection. To address these challenges, we propose the Precision Lasso. Precision Lasso is a Lasso variant that promotes sparse variable selection by regularization governed by the covariance and inverse covariance matrices of explanatory variables. Our results indicate that in settings with correlated and linearly dependent variables, the Precision Lasso outperforms popular methods.