A method for processing data includes receiving in a peripheral device, which is connected by a bus to a host processor having host resources, a notification of a sleep state of at least one of the host resources. While the at least one of the host resources is in the sleep state, when the peripheral device receives data from a data source for delivery to the host processor, the peripheral device sends a message to the data source, which causes the data source to defer conveying further data to the peripheral device until the at least one of the host resources has awakened from the sleep state.