Recent research demonstrates that white matter of the brain contains not only long T2 components, but a minority of ultrashort T2* components. Adiabatic inversion recovery prepared dual echo ultrashort echo time (IR-dUTE) sequences can be used to selectively image the ultrashort T2* components in white matter of the brain using a clinical whole body scanner. The T2*s of the ultrashort T2* components can be quantified using mono-exponential decay fitting of the IR-dUTE signal at a series of different TEs. However, accurate T1 measurement of the ultrashort T2* components is technically challenging. Efficient suppression of the signal from the majority of long T2 components is essential for robust T1 measurement. In this paper we describe a novel approach to this problem based on the use of IR-dUTE data acquisitions with different TR and TI combinations to selectively detect the signal recovery of the ultrashort T2* components. Exponential recovery curve fitting provides efficient T1 estimation, with minimized contamination from the majority of long T2 components. A rubber phantom and a piece of bovine cortical bone were used for validation of this approach. Six healthy volunteers were studied. An averaged T2* of 0.32 ± 0.09 ms, and a short mean T1 of 226 ± 46 ms were demonstrated for the healthy volunteers at 3T.