In robotic systems, perception latency is a term that refers to the computing time, measured from the data acquisition to the moment in which perception output is ready to be used to compute control commands. There is a clear compromise between perception latency and the stability of the overall robotic system, referred here as the latency-precision trade-off. Opposed to periodic sampling, which forces a particular perception latency, we study for the first time the computation of the best sequence of latencies, obtaining different precision at different moments in time. Using this concept we give a formal problem formulation of the attention-precision trade-off. Moreover, we give a method to obtain sequences of latencies that improve the system performance which is verified by simulation experiments.