A method of refreshing a memory device includes performing normal refresh operations on memory cell rows in response to a refresh command and performing self-refresh operations on the memory cell rows according to a refresh clock signal in response during a self-refresh mode of the memory device between a self-refresh enter command and a self-refresh exit command. The refresh clock signal has a first self-refresh cycle before the self-refresh begins and a second self-refresh cycle, which may be longer than the first self-refresh cycle, after the self-refresh begins. In some examples, no self-refresh may be performed by the memory device during a self-refresh mode.