A method aims at controlling parameters used by communication terminals of a telecommunication system which enables discontinuous reception. The discontinuous reception involves DRX cycles during each one of which a communication terminal wakes up at least once to monitor a downlink control channel. The telecommunication system enables the use of DRX cycles of different lengths. The method includes a determining procedure (s10) comprising determining, on a per communication terminal basis, whether the communication terminal is eligible to rely on a terminal-controlled mobility procedure, wherein determining is based on at least one characteristic of the communication terminal. The method also includes a setting procedure (s20) comprising, at least for one of the possible outcomes of the determining procedure (s10), setting one or more parameters on the communication terminal accordingly.