The Fluid And White matter Suppression (FLAWS) MRI sequence provides multiple T1-weighted contrasts of the brain in a single acquisition. However, the FLAWS acquisition time is approximately 8min with a standard GRAPPA 3 acceleration factor at 3T. This study aims at reducing the FLAWS acquisition time by providing a new sequence optimization based on a Cartesian phyllotaxis k-space undersampling and a compressed sensing (CS) reconstruction. This study also aims at showing that T1 mapping can be performed with FLAWS at 3T. The CS FLAWS parameters were determined using a method based on a profit function maximization under constraints. The FLAWS optimization and T1 mapping were assessed with in-silico, in-vitro and in-vivo (10 healthy volunteers) experiments conducted at 3T. In-silico, in-vitro and in-vivo experiments showed that the proposed CS FLAWS optimization allows the acquisition time of a 1mm-isotropic full-brain scan to be reduced from [Formula: see text] to [Formula: see text] without decreasing image quality. In addition, these experiments demonstrate that T1 mapping can be performed with FLAWS at 3T. The results obtained in this study suggest that the recent advances in FLAWS imaging allow to perform multiple T1-weighted contrast imaging and T1 mapping in a single [Formula: see text] sequence acquisition.