Although experimental work on environmental enrichment has answered many important questions, it is not yet known whether beneficial effects of enrichment are more strongly influenced by regular provision of novel objects, or by the diversity of objects present at any one time. In a five-replicate study, 80 newly weaned male Wistar rats were housed in groups of four in: a ‘novelty’ condition (NC) in which five copies of the same object were provided in the home cage during the first week of the study followed by five copies of a different, novel, object over each of the next 4 weeks; a ‘complexity’ condition (CC) in which one example of each of the five objects used in NC was always present in the cage across the 5-week study period. Behaviour was collected in two 2-h sessions every week, once during the light phase of the light/dark cycle and once during the dark phase. Body weight and weight gain were measured over the five weeks and organ weights were recorded post-mortem. Rats in the CC displayed elevated levels of measures suggestive of improved welfare such as sleep, enrichment-directed behaviour, enrichment contact, weight gain and relative thymus weight, and decreased levels of indicators denoting poor welfare including aggression, awake-non active and audible vocalizations. It appears that CC may have the potential to increase the frequency and diversity of behaviours, to express different types of behaviour when desired, and to augment the ability of the animals to exert some control over their environment, findings that may improve their welfare. Provision of novelty per se in the absence of diversity of objects at any one time seems to be less beneficial. Order (replicate) effects in the NC group indicated that responses of the animals towards the enrichment regimen appeared to depend on the type of object supplied, thus drawing attention to the importance of object characteristics when designing enrichment protocols for laboratory animals.