Security in wireless sensor networks is commonly based on symmetric encryption and requires key-management systems to establish and exchange secret keys. A constraint that is common to many key-management approaches is an upper bound to the total number of nodes in the network. An example is represented by the schemes based on combinatorial design. These schemes use specific rules for the generation of sets of keys that are distributed to the nodes before deploying the network. The aim of these approaches is to improve the resilience of the network. However, the quantity of data that must be stored by each node is proportional to the number of nodes of the network, so the available memory affects the applicability of these schemes. This paper investigates the opportunity of reducing the storage overhead by distributing the same set of keys to more than one node. In addition, the presence of redundant sets of keys affects the resilience and the security of the network. A careful analysis is conducted to evaluate benefits and drawbacks of redundant key distribution approaches. The results show that the use of redundancy decreases the level of resilience, but it scales well on very large networks.