A machine tool has a spindle with a splayed taper at the tool-holding tip, the taper expanding outwards in the direction away from the supporting bearings. Due to centrifugal forces, any cutting fluid (scattered by cutting operations) that reaches the surface of the taper tends to move on the surface of the taper and scatter away from the bearing, avoiding the intrusion of cutting fluid into the bearing. A flange having an internal taper matching the splayed taper of the tool-holding tip can be provided around the tip, making it more difficult for cutting fluid to reach the clearance between the tapers and further encouraging any intruding fluid to move and scatter away from the bearing.