The deleterious effects of inbreeding can be substantial in wild populations and mechanisms to avoid such matings have evolved in many organisms. In situations where social mate choice is restricted, extrapair paternity may be a strategy used by females to avoid inbreeding and increase offspring heterozygosity. In the cooperatively breeding Seychelles warbler, Acrocephalus sechellensis, neither social nor extrapair mate choice was used to avoid inbreeding facultatively, and close inbreeding occurred in approximately 5% of matings. However, a higher frequency of extragroup paternity may be selected for in female subordinates because this did reduce the frequency of mating between close relatives. Inbreeding resulted in reduced individual heterozygosity, which, against expectation, had an almost significant (P = 0.052), positive effect on survival. Conversely, low heterozygosity in the genetic mother was linked to reduced offspring survival, and the magnitude of this intergenerational inbreeding depression effect was environment-dependent. Because we controlled for genetic effects and most environmental effects (through the experimental cross-fostering of nestlings), we conclude that the reduced survival was a result of maternal effects. Our results show that inbreeding can have complicated effects even within a genetic bottlenecked population where the “purging” of recessive alleles is expected to reduce the effects of inbreeding depression.