The invention relates to mobility management nodes and methods of the mobility management nodes of enabling delivery of a Mobile Terminating (MT) Short Message (SM) to a mobile terminal. In a first aspect of the invention, a method of a mobility management node is provided for enabling delivery of a MT SM to a mobile terminal which currently is in extended idle mode Discontinuous Reception (eDRX) mode. The method comprises receiving an indication from a Short Message Service Gateway Mobile Switching Centre (SMS-GMSC) that the SM is to be delivered, receiving a notification that the mobile terminal has exited an eDRX mode before a paging occasion has occurred, and submitting, in response to the notification, a message indicating to the SMS-GMSC that the mobile terminal is available for delivery of the SM.