Zero-phonon hole (ZPH) growth kinetics data that span six decades of burn fluence are reported for Al-phthalocyanine tetrasulphonate (APT) in hyperquenched glassy water (HGW) at 5.0 K. The kinetics are highly dispersive. The hole growth equation used for analysis of the dispersion incorporates three distributions (lambda, alpha, and omega) where lambda is the tunnel parameter associated with nonphotochemical hole burning (NPHB), alpha is the angle between the transition dipole and the laser polarization and the omega -distribution stems from off-resonant absorption of the zero-phonon line (ZPL). The single site absorption profile used includes the phonon sideband as well as the ZPL. The homogeneous width of the ZPL and shape of the phonon sideband were determined from experiment. Eight models, which include the possible combinations of the above distributions, were used to fit the data. As in previous works the lambda -distribution was taken to be a Gaussian peaked at lambda=lambda (0) with a standard deviation of sigma (lambda). The results show that the contribution to the dispersive kinetics from the lambda -distribution is of primary importance. It provides a good fit to the data over the first three decades of burn fluence (similar to 80% of the saturated ZPH depth). The intrinsic contributions from the alpha- and omega -distributions become important for the last similar to 20% of the burn. These two distributions by themselves or in combination yielded poor fits to the data. The three distributions in combination (lambda alpha omega -model) provided a good fit over the first five decades of burn fluence. Importantly, the lambda (0) and sigma (lambda) values of 8.3 and 0.95 from the lambda -distribution alone are nearly the same as those from the lambda alpha omega -distribution. The above findings for APT/HGW should be widely applicable since previous studies of other NPHB systems led to sigma (lambda) values greater than or similar to1. It is emphasized that APT/HGW is an ideal system for hole growth studies because of its very narrow ZPL and weak electron-phonon coupling (S similar to0.2) and because it satisfies the homogeneity condition, i.e., all sites are burnable.