The modeling approach of B. L. Sawford and F. H. Guest ("8th Symposium of Turbulence and Diffusion; San Diego, CA," pp. 96-99. Am. Meteorol. Soc., Boston, MA, 1990) is extended to encompass the formulation of Lagrangian stochastic models for fluid velocities along heavy-particle trajectories in inhomogeneous turbulent flows. The approach ensures consistency with prescribed Eulerian fluid velocity statistics. Models are formulated and then used in conjuction with the equations of motion for heavy particles to simulate the trajectories of heavy particles in vertical turbulent pipe flow. Model predictions for particle-velocity statistics, particle deposition velocities, and mean particle concentrations are shown to be in good agreement with experimental results. In contrast with "eddy-interaction" models but in accord with the results of direct numerical simulations, the models predict a buildup of mean particle concentration within the viscous sublayer at y + β 0.2. It is suggested that Lagrangian stochastic models for fluid-particle motions provide a good description of fluid velocities along the trajectories of heavy particles, when Lagrangian timescales are appropriately modified.