A seal comprises the combination of a primary seal and a secondary seal each of which acts on at least one shoe that is installed with clearance relative to one of a rotor and a stator in a position to create a non-contact seal therewith. The at least one shoe is provided with a surface geometry and labyrinth-type teeth that influence the inertia of fluid flowing across the seal, and, hence, the velocity of the fluid and the pressure distribution across the seal, ultimately affecting the balance of forces applied to the seal.