The signal strength available to a mobile unit is periodically monitored (21), and if it falls below a threshold value X(off) the handset (40) determines whether the signal strength on an alternative network is greater than a value Y(on). If such a connection is available, a handover attempt is initiated (3). If the handover attempt (3) fails (step 4), the relevant threshold value X(off) and Y(on), depending on the cause of failure, is then raised (40) so that future handoffs are not attempted in those same conditions. If the call fails in these circumstances, the caller will have to establish a new call (step 1). If the handover is successful, (step 5) then one or both of the handover thresholds (X(off), Y(on)) may be lowered (step 51), allowing future handovers to take place more promptly. Lowering may be done in smaller increments than increases, or less frequently. By varying the threshold values empirically more efficient handover can be achieved than by pre-setting a permanent value.