In the new generation of torque converter automatic transmissions (ATs), characterized by a high number of gears, multi-step gear shifts may be executed frequently in order to improve the driving performance. They include double-transition shifts (DTSs), which require close coordination between multiple control inputs (e.g. torque capacities of four clutches and engine torque). The previously developed AT control trajectory optimization tool is utilized in this paper for the purpose of DTS control optimization including engine torque control. With the aim to gain insights into optimal control action and coordination, six different DTS control strategies are proposed and assessed. These strategies are incorporated into the optimization problem formulation through additional, shift phase-related constraints that the optimization algorithm needs to satisfy. In this way, control strategies with different degrees of complexity and applicability can be quantitatively assessed in terms of achievable shift performance. The proposed strategies have been examined on an example of characteristic DTS downshift of an advanced 10-speed AT. Based on the summarized optimization results obtained for different levels of clutch energy loss penalization, it has been found that the strategy characterized with quick release of the off-going clutches can provide an optimal compromise between shift comfort performance and energy loss reduction.