Neutral pumping rates are calculated for pump-limiter and divertor options of a next step tokamak ignition device using a method that accounts for the coupled effects of neutral transport and plasma transport. For both pump limiters and divertors the plasma flow into the channel surrounding the neutralizer plate is greatly reduced by the neutral recycling. The fraction of this flow that is pumped can be large (>50%) but in general is dependent on the particular geometry and plasma conditions. It is estimated that pumping speeds ≳105 L/s are adequate for the exhaust requirements in the pump-limiter and the divertor cases.