In this paper we propose a new strong and perfectly key-insulated signature scheme, more efficient than previous proposals and whose key length is constant and independent of the number of insulated time periods. Moreover, unlike previous schemes, it becomes forward-secure when all the existing secrets at a given time period are compromised. We also present a variant forwardsecure scheme in which an adversary needs to compromise a user at a second time period before being able to compute future secret keys.