The influence of the boundary conditions on convective instability in rapidly (10−5<E< 10−3) rotating spherical shells is investigated. For the purpose of comparison, both stress-free and rigid boundaries are studied at exactly the same parameter range of the problem. In the rigid boundary case an Ekman boundary layer is formed in middle latitudes where columnar convective rolls meet the outer spherical surface. There is also a boundary layer at the equatorial region of the inner sphere where the rolls are attached. When the Prandtl numberPr≥ O(1), the Ekman boundary layer produced by the rigid boundaries has a destabilizing effect, the critical Reyleigh number being substantially reduced. The value of the critical azimuthal wavenumber and the drifting rate of the convection rolls are also significantly lower compared wilh the free boundary case. When the Prandtl numberPr< O(1), so thermal dissipation dominates over the viscous dissipation, the Ekman boundary layers exhibit a stabilizing effect. Convection in a rotating annulus including the effect of the Ekman layers is investigated analytically, and shows similar behaviour to that of the spherical shells. The influence of varying aspect ratio is also discussed.