Sleep is ubiquitous in animals, but there is great inter- and intraspecific variation in the daily amount of sleep that is needed. Chronic sleep curtailment or experimental sleep deprivation are known to impair health and performance of individuals, but not much is known about the fitness consequences of naturally occurring variation in sleep behaviour. Here we test for assortative mating in sleep behaviour and for correlations between sleep phenotypes and reproductive success and survival in a free-living blue tit population. We found that partners of a social breeding pair were mated assortatively in regard to standardized awakening time, i.e. awakening time relative to that of other birds of the same sex in the population. We found no evidence for assortative mating for other sleep parameters. In female blue tits no sleep parameter that we measured was significantly correlated with lay date or clutch size. Females that had extra-pair young in their brood did not differ in awakening time, or in any other sleep parameter, compared to females without extra-pair young. In males, the probability of siring extra-pair young was related to sleep onset and sleep duration, but not as predicted. Males that began to sleep earlier and slept longer were more likely to sire extra-pair offspring. None of the sleep parameters were significantly correlated with local survival of first-year birds. Our results suggest that there is no strong effect of variation in sleep behaviour on fitness in blue tits, at least under natural conditions. Such a relationship might only become evident when natural sleep patterns are experimentally disturbed, or when sleep quality is affected by anthropogenic noise or light pollution.