To capture the effects of mesoscale turbulent eddies, coarse-resolution Eulerian ocean models resort to tracer diffusion parameterizations. Likewise, the effect of eddy dispersion needs to be parameterized when computing Lagrangian pathways using coarse flow fields. Dispersion in Lagrangian simulations is traditionally parameterized by random walks, equivalent to diffusion in Eulerian models. Beyond random walks, there is a hierarchy of stochastic parameterizations, where stochastic perturbations are added to Lagrangian particle velocities, accelerations, or hyper-accelerations. These parameterizations are referred to as the 1st, 2nd and 3rd order ‘Markov models’ (Markov-N), respectively. Most previous studies investigate these parameterizations in two-dimensional setups, often restricted to the ocean surface. On the other hand, the few studies that investigated Lagrangian dispersion parameterizations in three dimensions, where dispersion is largely restricted to neutrally buoyant surfaces, have focused only on random walk (Markov-0) dispersion. Here, we present a three-dimensional isoneutral formulation of the Markov-1 model. We also implement an anisotropic, shear-dependent formulation of random walk dispersion, originally formulated as a Eulerian diffusion parameterization. Random walk dispersion and Markov-1 are compared using an idealized setup as well as more realistic coarse and coarsened (50 km) ocean model output. While random walk dispersion and Markov-1 produce similar particle distributions over time when using our ocean model output, Markov-1 yields Lagrangian trajectories that better resemble trajectories from eddy-resolving simulations. Markov-1 also yields a smaller spurious dianeutral flux.