This paper proposes three key agreement protocols that emphasize their security and performance. First, the two-pass authenticated key agreement (AK) protocol is presented in the asymmetric setting, which is based on Diffie-Hellman key agreement working over an elliptic curve group and provides more desirable security attributes than the MTI/A0, two-pass Unified Model and two-pass MQV protocols. Other two protocols are modifications of this protocol: the three-pass authenticated key agreement with key confirmation (AKC) protocol which uses message authentication code (MAC) algorithms for key confirmation, and the two-pass authenticated key agreement protocol with unilateral key confirmation which uses the MAC and the signature.