  Self-avoidance is a common mechanism to improve the efficiency of a random
walker for covering a spatial domain. However, how this efficiency decreases
when self-avoidance is impaired or limited by other processes has remained
largely unexplored. Here we use simulations to study the case when the
self-avoiding signal left by a walker both (i) saturates after successive
revisits to a site, and (ii) evaporates, or dissappears, after some
characteristic time. We surprisingly reveal that the mean cover time becomes
minimum for intermediate values of the evaporation time, leading to the
existence of a nontrivial optimum management of the self-avoiding signal. We
argue that this is a consequence of complex blocking effects caused by the
interplay with the signal saturation and, remarkably, we show that the optimum
becomes more and more significant as the domain size increases.
