We propose a method that allows for dexterous manipulation of an object by exploiting contact with an external surface. The technique requires a compliant grasp, enabling the motion of the object in the robot hand while allowing for significant contact forces to be present on the external surface. We show that under this type of grasp it is possible to estimate and control the pose of the object with respect to the surface, leveraging the trade-off between force control and manipulative dexterity. The method is independent of the object geometry, relying only on the assumptions of type of grasp and the existence of a contact with a known surface. Furthermore, by adapting the estimated grasp compliance, the method can handle unmodelled effects. The approach is demonstrated and evaluated with experiments on object pose regulation and pivoting against a rigid surface, where a mechanical spring provides the required compliance.