The class of strong failure detectors (denoted S) includes all failure detectors that suspect all crashed processes and that do not suspect some (a priori unknown) process that never crashes. So, a failure detector that belongs to S is intrinsically unreliable as it can arbitrarily suspect correct processes. Several S-based consensus protocols have been designed. Some of them systematically require n computation rounds (n being the number of processes), each round involving n2 or n messages. Others allow early decision (i.e., the number of rounds depends on the maximal number of crashes when there are no erroneous suspicions) but require each round to involve n2 messages. This paper presents an early deciding S-based consensus protocol each round of which involves 3(n-1) messages. So, the proposed protocol is particularly time and message-efficient. Moreover, it can easily be generalized to reduce the number of rounds at the price of an increase in the number of messages per round.