Test-particle transport arising from E 3 B motion in a turbulent plasma is investigated numerically. The electrostatic field is determined by solving the Hasegawa-Mima model for two-dimensional drift turbulence. In the linear regime the particles experience stochastic diffusion, but in the fully nonlinear, strongly turbulent regime the diffusion rate is greatly reduced. Finite Larmor radius effects, relevant to alpha-particle transport in tokamaks, are also shown to strongly inhibit the level of transport.