The Carnot-like heat engines are classified into three types (normal-, sub- and, super-dissipative) according to relations between the minimum irreversible entropy production in the “isothermal” processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between η C /2 and η C /(2 η C ), η C /2 and η C , 0 and η C /(2 η C ), respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Lett. 98 (2012) 40001] although the dissipative engines and the irreversible ones are inequivalent to each other. The Carnot-like heat engines are classified into three types (normal-, sub- and, super-dissipative) according to the minimum irreversible entropy production in the “isothermal ” processes and the time for completing those processes. at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between η C / 2 and η C / (2 η C), η C / 2 and η C, 0 and η C / (2 η C), respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Lett. 98 (2012) 40001] although the dissipative engines and the irreversible ones are inequivalent to each other.