Abstract: Apparatus and method for tightening assemblies held together by threaded fasteners. Prior to tightening, the gradients of a selected number of possible torque-rotation curves for the assembly are established and stored along with the associated tightening torques required to induce a desired preload in the fastener when the assembly is tightened according to the selected torque-rotation curves. As torque and rotation are imparted to the fastener to tighten the assembly, the gradient of the actual torque-rotation curve through which the assembly is taken is calculated. The calculated gradient is compared with the stored gradients to derive that tightening torque which is associated with that stored gradient closest in magnitude to the calculated gradient. The derived tightening torque is used to control the torque applied to the fastener.