The basic two-terminal key generation model is considered, where the communication between the terminals is limited. We introduce a preorder relation on the set of joint distributions called XY-absolute continuity, and we reduce the multi-letter characterization of the key-communication tradeoff to the evaluation of the XY-concave envelope of a functional. For small communication rates, the key bits per interaction bit is expressed with a 'symmetrical strong data processing constant'. Using hypercontractivity and Rényi divergence, we also prove a computationally friendly strong converse bound for the common randomness bits per interaction bit in terms of the supremum of the maximal correlation coefficient over a set of distributions, which is tight for binary symmetric sources. Regarding the other extreme case, a new characterization of the minimum interaction for achieving the maximum key rate (MIMK) is given, and is used to resolve a conjecture by Tyagi  about the MIMK for binary sources.