The pressure drag of blunt bluff bodies is highly relevant in many practical applications, including to the aerodynamic drag of road vehicles. This paper presents theory revealing that a mean drag reduction can be achieved by manipulating wake flow fluctuations. A linear feedback control strategy then exploits this idea, targeting attenuation of the spatially integrated base (back face) pressure fluctuations. Large-eddy simulations of the flow over a D-shaped blunt bluff body are used as a test-bed for this control strategy. The flow response to synthetic jet actuation is characterised using system identification, and controller design is via shaping of the frequency response to achieve fluctuation attenuation. The designed controller successfully attenuates integrated base pressure fluctuations, increasing the time-averaged pressure on the body base by 38%. The effect on the flow field is to push the roll-up of vortices further downstream and increase the extent of the recirculation bubble. This control approach uses only body-mounted sensing/actuation and input-output model identification, meaning that it could be applied experimentally.