  We extend our previous study on the effects of an information-theoretically
motivated nonlinear correction to the Wheeler-deWitt equation in the
minisuperspace scheme for FRW universes. Firstly we show that even when the
geometry is hyperbolic, and matter given by a cosmological constant, the
nonlinearity can still provide a barrier to screen the initial singularity,
just as in the case for flat universes. Secondly, in the flat case we show that
singularity avoidance in the presence of a free massless scalar field is
perturbatively possible for a very large class of initially unperturbed quantum
states, generalising our previous discussion using Gaussian states.
