Pneumatic tightening tools can be used for high speed assembly of critical bolts to precise loads by dynamically controlling the output power of the pneumatic tool during a tightening cycle using an electronically controlled air pressure regulator to reduce the tightening rate, or the load increase per impact for impact or impulse tools, to enable the tool to be stopped precisely at a specified stopping load or torque. For prevailing torque fasteners, the output power of the pneumatic tool is dynamically controlled to minimize the speed of rotation during rundown, to minimize the heating effects associated with such torque fasteners, and to then increase the power from the tool, as required, to provide the torque to reach the specified stopping load or torque. The maximum air pressure supplied to the pneumatic tool can be limited, depending on the expected torque required to tighten the fastener to the specified load or torque.