Neoclassical and resonant transport in tandem mirrors is considered in the limit where the collision frequency νc exceeds the bounce frequency νb for solenoid ions. Approximate expressions for the diffusion coefficient are obtained analytically and verified by using a random walk code. These expressions scale as νc, (νc/νd)1/2 νb, or νb depending on the value of the azimuthal drift frequency νd. The connection to regimes of lower collisionality is described. In particular, for neoclassical transport (νd/νb≪1) at moderate collisionality, a mechanism previously described but not generally known leads to a term in the diffusion coefficient which scales as νc and allows smooth matching to the high-collisionality regime.