Studies of the Interact traffic at the level of network prefixes, fixed length prefixes, TCP flows, AS's, and WWW traffic, have all shown that a very small percentage of the flows carries the largest part of the information. This behavior is commonly referred to as" the elephants and mice phenomenon". Traffic engineering applications, such as re-routing or load balancing, could exploit this property by treating elephant flows differently. In this context, though, elephants should not only contribute significantly to the overall load, but also exhibit sufficient persistence in time. The challenge is to be able to examine a flow's bandwidth and classify it as an elephant based on the data collected across all the flows on a link. In this paper, we present a classification scheme that is based on the definition of a separation threshold, that elephants have to exceed. We introduce two single-feature classification schemes, and show that the resulting elephants are highly volatile. We then propose a two-feature classification scheme that incorporates temporal characteristics and show that this approach is more successful in isolating elephants that exhibit consistency-thus making them more attractive for traffic engineering applications.