A first wireless communication device belongs to a first of multiple groups of wireless communication devices. Devices in any given group are synchronized to the same timing reference and devices in different groups are not synchronized to the same timing reference. The first device receives a message that indicates, for each of one or more of the groups, a range of possible values for misalignment between the timing reference of that group and a common timing reference. The range accounts for uncertainty in that misalignment. The first device determines, based on the one or more ranges, intervals of times during which direct control signaling is expected to be received at the first device from one or more devices in one or more other groups. The first device then adjusts intervals of times during which it is configured to operate in an awake state to narrowly encompass the intervals of times during which the direct control signaling is expected to be received.