An important class of floating wave energy converters (that includes the IPS buoy, the Wavebob and the PowerBuoy) comprehends devices in which the energy is converted from the relative (essentially heaving) motion between two bodies oscillating differently. The paper considers the case of the IPS buoy, consisting of a floater rigidly connected to a fully submerged vertical (acceleration) tube open at both ends. The tube contains a piston whose motion relative to the floater-tube system (motion originated by wave action on the floater and by the inertia of the water enclosed in the tube) drives a power take-off mechanism (PTO) (assumed to be a linear damper). To solve the problem of the end-stops, the central part of the tube, along which the piston slides, bells out at both ends to limit the stroke of the piston. The use of a hydraulic turbine inside the tube is examined as an alternative to the piston. A frequency domain analysis of the device in regular waves is developed, combined with a one-dimensional unsteady flow model inside the tube (whose cross section is in general non-uniform). Numerical results in regular and irregular waves are presented for a cylindrical buoy with a conical bottom, including the optimization of the acceleration tube geometry and PTO damping coefficient for several wave periods.