In recent years, a large number of identity-based key agreement protocols from pairings have been proposed. Some of them are elegant and practical. However, the security of this type of protocol has been surprisingly hard to prove, even in the random oracle model. The main issue is that a simulator is not able to deal with reveal queries, because it requires solving either a computational problem or a decisional problem, both of which are generally believed to be hard (i.e., computationally infeasible). The best solution so far for security proofs uses the gap assumption, which means assuming that the existence of a decisional oracle does not change the hardness of the corresponding computational problem. The disadvantage of using this solution to prove security is that such decisional oracles, on which the security proof relies, cannot be performed by any polynomial time algorithm in the real world, because of the hardness of the decisional problem. In this paper we present a method incorporating a built-in decisional function into the protocols. The function transfers a hard decisional problem in the proof to an easy decisional problem. We then discuss the resulting efficiency of the schemes and the relevant security reductions, in the random oracle model, in the context of different pairings one can use. We pay particular attention, unlike most other papers in the area, to the issues which arise when using asymmetric pairings.