We study two encodings of the asynchronous ß-calculus with input-guarded choice into its choice-free fragment. One encoding is divergence-free, but refines the atomic commitment of choice into gradual commitment. The other preserves atomicity, but introduces divergence. The divergent encoding is fully abstract with respect to weak bisimulation, but the more natural divergence-free encoding is not. Instead, we show that it is fully abstract with respect to coupled simulation, a slightly coarser---but still coinductively defined---equivalence that does not enforce bisimilarity of internal branching decisions. The rigorous correctness proofs for the two choice encodings introduce a novel proof technique exploiting the properties of explicit decodings from translations to source terms. This paper is a revised full version of a technical report that appeared as IMMD-VII-01/96 at University of Erlangen and TR 342 at University of Cambridge. An extended summary appeared in the Proceedings ..