We investigated approaches to reducing the dose in CT without impairing image quality. Dose can be reduced for non-circular object cross-sections without a significant increase in noise if X-ray tube current is reduced at angular tube positions where the X-ray attenuation by the patients is small. We investigated different schemes of current modulation during tube rotation by simulation and phantom measurements. Both pre-programmed sinusoidal modulation functions and attenuation-based on-line control of the tube current were evaluated. All relevant scan parameters were varied, including constraints such as the maximum modulation amplitude. A circular, an elliptical and two oval water phantoms were used. Results were validated on six cadavers. Dose reduction of 10-45% was obtained both in simulations and in measurements for the different non-circular phantom geometries and current modulation algorithms without an increase in pixel noise values. On-line attenuation-based control yielded higher reductions than modulation by a sinusoidal curve. The maximal dose reduction predicted any simulations could not be achieved due to limits in the modulation amplitude. In cadaver studies, a reduction of typically 20-40% was achieved for the body and about 10% for the head. Variations of our technique are possible; a slight increase in nominal tube current for high-attenuation projections combined with attenuation-based current modulation still yields significant dose reduction, but also a reduction in the structured noise that may obscure diagnostic details. We conclude that a significant reduction in dose can be achieved by tube current modulation without compromising image quality. Attenuation-based on-line control and a modulation amplitude of at least 90% should be employed.