Neoclassical transport of minority suprathernial alpha particles is investigated. This work departs from previous investigations in that (a) the banana-width ordering parameter ρθ/L is not formally restricted to be a small parameter and (b) a linearized collision operator that retains the effects of pitch-angle scattering, electron and ion drag, and speed diffusion is used. A step model approximation for the large-aspect-ratio, circular-cross-section tokamak magnetic field is adopted to simplify the orbit-averaging procedure. Assuming that the suprathermal alphas are in the banana regime, an asymptotic expansion in τB/τs ≪ 1 is carried out. The lowest order distribution is independent of poloidal angle on a drift surface and is completely determined by solving an orbit-averaged drift kinetic equation, A variational problem is derived that is equivalent to this three-dimensional, inhomogeneous differential equation. A similar procedure yields an expression for the first-order component f1. Knowledge of f1 is sufficient to obtain expressions for particle and heat fluxes directly from the definitions or from alternate expressions. Extension of this model to account for loss regions in phase space is outlined.