Developing a relevant model for brain gray matter is a complex task. As opposed to white matter, features such as inter-compartment water exchange or soma should likely be modeled. In this work we examine the performance of a variant of the Kärger Model, called GRAMMI, that accounts for exchange, both on synthetic and experimental data. We show q-t coverage is necessary for reliable model parameter estimation at the individual voxel level and compare two regression approaches. Future work includes protocol optimization and the extension of the GRAMMI model to account for soma.