We investigate a number of issues related to identity based authenticated key agreement protocols in the Diffie-Hellman family enabled by the Weil or Tate pairings. These issues include how to make protocols efficient; to avoid key escrow by a Trust Authority (TA) who issues identity based private keys for users, and to allow users to use different TAs. We describe a few authenticated key agreement (AK) protocols and AK with key confirmation (AKC) protocols by modifying Smart's AK protocol [26]. We discuss the security of these protocols heuristically and give formal proofs of security for our AK and AKC protocols (using a security model based on the model defined in [13]). We also prove that our AK protocol has the key compromise impersonation property. We also show that our second protocol has the TA forward secrecy property (which we define to mean that the compromise of the TA's private key will not compromise previously established session keys), and we note that this also implies that it has the perfect forward secrecy property.