The strongly-modified turbulence statistics of Rayleigh-Bénard convection subject to various rotation rates is addressed by numerical investigations. The flow is simulated in a domain with periodic boundary conditions in the horizontal directions, and confined vertically by parallel no-slip isothermal walls at the bottom and top. Steady rotation is applied about the vertical. The rotation rate, or equivalently the Rossby number Ro, is varied such that Ro ranges from 8 (no rotation) to Ro = 0.1 (strong rotation). Two different Rayleigh numbers are used, viz. Ra = 2.5 × 106 and 2.5 × 107, characterising buoyancy due to temperature differences. The Prandtl number s = 1, close to the value for air. Horizontally averaged statistics show that rotation reduces the turbulence intensity, although probability density functions clearly show that considerable (preferably cyclonic) vorticity is added to the flow by the Ekman boundary layers on the solid walls. Rotation changes the balance of the turbulent kinetic energy budget. It is found that for a range of rotation rates the buoyant production is higher than without rotation. Therefore, at appropriate rotation rates the heat flux through the fluid layer is increased relative to the non-rotating case. At sufficiently rapid rotation, however, the heat flux through the fluid layer is strongly attenuated.