Selective eta-expansion is a powerful \binding-time improvement", i.e., a source- program modication that makes a partial evaluator yield better results. But like most binding- time improvements, the exact problem it solves and the reason why have not been formalized and are only understood by few. In this paper, we describe the problem and the eect of eta-redexes in terms of monovariant binding-time propagation: eta-redexes preserve the static data o w of a source program by inter- facing static higher-order values in dynamic contexts and dynamic higher-order values in static contexts. They contribute to two distinct binding-time improvements. We present two extensions of Gomard's monovariant binding-time analysis for the pure -calculus. Our extensions annotate and eta-expand -terms. The rst one eta-expands static higher-order values in dynamic contexts. The second also eta-expands dynamic higher-order values in static contexts. As a signican t application, we show that our rst binding-time analysis suces to reformulate the traditional formulation of a CPS transformation into a modern one-pass CPS transformer. This binding-time improvement is known, but it is still left unexplained in contemporary literature, e.g., about \cps-based" partial evaluation. We also outline the counterpart of eta-expansion for partially static data structures.