The equations of motion for a sediment grain near a noncohesive bed and those for the local fluid flow are combined to produce a set of differential equations that can be solved numerically to describe the trajectory of a saltating grain as a function of time. The lift coefficient is set based on a reanalysis of data produced by Chepil, and the other parameters of the problem are set using standard fluid mechanical relationships: the initial velocity and position are specified with a separate model. The heights of the resulting trajectories are found to be significantly lower than available measurements would indicate; therefore two extensions of the model are examained; the effect that spin lift and form lift have on a series of trajectories, and the effect of partially elastic collisions between a moving grain and the bed over which it is traveling. A model that includes the second process is less complicated than one that includes the first, and it yields trajectories that agree very well with available experimental measurements when a rebound coefficient that varies around 0.5 and depends on the impact momentum is used. We conclude that the model provides a reasonable representation of saltation in water and that both fluid-solid and solid-solid interactions are required to reproduce the parameters of measured trajectories.