A method reduces a time delay or lag between a commanded upshift and a resultant upshift event in vehicle. The method detects the commanded upshift, calculates a scheduled engine torque reduction torque value as a function of an unmanaged torque, and reduces an input torque value from the engine using the calculated scheduled torque. A powertain includes an engine, a transmission, a torque converter, clutches that are selectively engageable to provide at least six forward speed ratios, a reverse speed ratio, and a neutral condition, and a controller. The controller has an algorithm controlling an operation of an off-going clutch and the on-coming clutch during a speed ratio change representing an upshift event. The algorithm calculates a scheduled torque value as a percentage of an unmanaged torque level of the engine, and controls the off-going and on-coming clutch through the speed ratio change using the calculated scheduled torque value.