T1 quantification of short-T2 species is challenging due to the uncommon behavior of the signal decay and magnetization tilting during excitations in conventional sequences. UTE sequences can therefore be considered with refined magnetization evolution models using the Bloch equations. In voxels comprising a mix of long and short-T2 components (e.g. myelin and water in the normal appearing white matter), an appropriate long-T2 suppression scheme is mandatory. In this work, we propose an analytical model to quantify the T1 of a short-relaxing component in an accelerated Inversion-Recovery UTE in vitro, and within long-T2 suppression condition.