Provided are techniques for transmitting blocks of data. It is determined whether any high priority out of sync (HPOOS) indicator is set to indicate that a number of modified segments associated with a block of data are less than or equal to a modified segments threshold. In response to determining that at least one high priority out of sync indicator is set, one or more sub-blocks of data in the modified segments associated with the block of data and with one set high priority out of sync indicator are transferred.