Q-space trajectory imaging (QTI) characterizes microstructures through the statistical moments of the diffusion tensor distribution. A constrained estimation framework named QTI+ was recently proposed to achieve mathematically and physically acceptable estimates of these moments. Here we consider expanding QTI+ with a new set of conditions based on the theoretical maximum value of water diffusivity. We show where these conditions are violated for different bulk diffusivity values, and how the new constraints affect the QTI scalar maps. The results show violations occurring almost exclusively in voxels containing gray matter and CSF. Imposing the constraints produces metrics closer to the expected values.