We propose a sticky transfer framework to enhance successful message transfers in a Delay- and Disruption-Tolerant Network (DTN). We propose a sticky transfer protocol within the framework that enables mobiles nodes to 'stick' to each other for a longer period of time in order to complete the transmissions of the messages needed to be sent. A mobile node A makes the decision of whether to stick to another node B or not by exchanging information with its neighbors and negotiating an agreement to stick to B in order to prolong the contact duration for transferring messages. Sticky transfers improve the number of successfully forwarded messages by allowing more messages to be transferred during the contact duration and by minimizing the number of message transfer aborts. We evaluate the effectiveness of the proposed sticky transfer framework through simulations, which show that the average message delivery ratio increased by as much as 38%, while the average end-to-end delay decreased by as much as 36% when using sticky transfers.