A high-pressure pump may include a cylinder, a plunger reciprocally driven by an eccentric to pressurize a pump chamber in the cylinder, a rider mounted on the eccentric to allow relative rotation of the eccentric, the rider presenting a face to the plunger, a tappet supported on the face of the rider for transmitting reciprocal movement from the rider to the plunger, and rotatable bearing elements that support the tappet for relative transverse movement of the face of the rider during operation of the pump. The rotatable bearing elements may be at least partially recessed in a body of the tappet. A common rail fuel injection system for an internal combustion engine comprising a common rail for distributing fuel to a plurality of fuel injectors associated with combustion cylinders of the engine may include such a pump for delivering fuel at high pressure to the common rail.