A method for communication in a receiver (20) includes receiving over a wireless communication channel a signal that carries at least a control channel. A first estimate of a response of the wireless communication channel is computed using a first estimation process having a first latency, and the control channel is decoded based on the first estimate. Upon identifying, based on the decoded control channel, a time period during which no data channel is to be addressed to the receiver, circuitry (24) of the receiver is shut down for at least part of the identified time period. A second estimate of the response is computed using a second estimation process having a second latency, higher than the first latency, and a data channel that is addressed to the receiver is decoded based on the second estimate.