A method of drilling a subterranean borehole comprising: a) pumping a drilling fluid down a drillstring (12), the drillstring (12) having a bit (14) at an end thereof, b) rotating the drillstring (12) about its longitudinal axis so that the bit forms a borehole (10) in the ground, the method further comprising the steps of: c) determining a desired drilling fluid flow rate range d) determining the desired upper and lower limits of the fluid pressure at the bottom of the wellbore (the BHP); e) determining the viscosity of drilling fluid which will maintain the BHP within the range set by the upper and lower BHP limits over the entire or the majority of the required drilling flow rate range; f) adjusting the composition of a drilling fluid to bring the drilling fluid to the viscosity calculated in step e above.