The majority of low field Magnetic Resonance (MR) analyses rely on T lifetime measurements. Modification of the T measurement to include a T dimension has made the T -T measurement a very powerful analytical technique. The T -T measurement is uniquely well suited to characterization of different spin populations in porous materials, such as fluid bearing reservoir rocks, and in soft biopolymer materials, for example foods. However, the T -T measurement is challenging or impossible if the T relaxation lifetime, or a component lifetime, is short-lived and the signal unobservable in an echo measurement. This occurs in many important classes of materials. A short lifetime T will not however, in general, preclude observation of a free induction decay with signal decay governed by T *. As outlined in this paper a T -T * measurement is a useful analog to the T -T experiment. T -T * measurement enables one to differentiate species as a function of T * in one dimension and T in the other dimension. Monitoring changes of the T -T * coordinate, and associated signal intensity changes, has the potential to reveal structural changes in materials evolving in time. These methods may also be employed to discriminate and identify solid-like species present in static samples. The T -T * measurement is very general in application, but in this paper we focus on cement-based mortars to develop and illustrate the essential ideas. T -T * results show a multi-modal behaviour of the MR signal lifetimes, T and T *, in mortar samples under study, indicating at least two different water populations. The short T * lifetime was assigned to interlayer water (water between C-S-H layers) where the associated T is also short lived. The longer T * lifetime was assigned to water in the pore space, where T is also longer lived. In addition to mortar samples we also show application of the method to a crystalline organic species, o-phenylenediamine, which features Sinc Gaussian and exponential decays of transverse magnetization.