A step-ratio automatic transmission is a system of torque converter, planetary gear sets, wet clutches and hydraulic control system to provide the flexibility in gear ratio selection. Gear shifting is realized by the engagement and disengagement of certain clutches which are commanded by control strategy through the hydraulic actuators. A complex interaction between components results in transient drive shaft torque, affecting shift quality. In particular, it is difficult to achieve fast upshift without inducing a large inertia torque spike due to changing speed ratios. A deep understanding of the kinematics and dynamics of the transmission during operation becomes critical to control clutches to enable fast and smooth gear shifting. This article performs detailed analytical study to explain the behaviors of a 10-speed automatic transmission by deriving the system’s governing equations. These equations show insights of working principles of the transmission and provide a new method to improve shift quality. Specifically, a managed tie-up between the on-coming and off-going clutches is introduced during the inertia phase. Shift simulations are conducted to systematically evaluate the effectiveness of the managed tie-up for suppressing the effects of inertia torque while shortening the inertia phase. The managed tie-up is implemented in a test vehicle through open loop control to demonstrate its feasibility.