  We analytically derive maximum efficiency at given cooling power for
Carnot-type low-dissipation refrigerators. The corresponding optimal cycle
duration depends on a single parameter, which is a specific combination of
irreversibility parameters and bath temperatures. For a slight decrease in
power with respect to its maximum value, the maximum efficiency exhibits an
infinitely-fast nonlinear increase, which is standard in heat engines, only for
a limited range of parameters. Otherwise, it increases only linearly with the
slope given by ratio of irreversibility parameters. This behavior can be traced
to the fact that maximum power is attained for vanishing duration of the hot
isotherm. Due to the lengthiness of the full solution for the maximum
efficiency, we discuss and demonstrate these results using simple
approximations valid for parameters yielding the two different qualitative
behaviors. We also discuss relation of our findings to those obtained for
minimally nonlinear irreversible refrigerators.
