We propose to estimate the active set associated with a standard linear Gaussian model when the design matrix is a n × p full-rank matrix (thus, n p). Asymptotic results are available for lasso-type estimators in the high-dimensional setting (n < p). In this paper, we present non-asymptotic results for estimation of the active set in small dimension by providing an explicit tuning parameter. Both theoretical and numerical arguments illustrate the benefits of our approach. An application to the detection of metabolites in metabolomic data is provided.