A system and method for modifying the engine pull-up (EPU) logic within a hybrid vehicle based on max motor torque that accounts for the drop or change in available motor torque due to the opening/slipping of a torque converter bypass clutch during engine starts is disclosed. An engine pull-up threshold is determined from max available motor torque at a virtual impeller speed, where the virtual impeller speed is the impeller speed that would result if the torque converter bypass clutch was open/slipping and transferring the same amount of torque.