String backgrounds associated with gauged G/H WZNW models in general d
epend nontrivially on alpha'. We note, however that there exists a loc
al covariant alpha'-dependent field redefinition that relates the exac
t metric-dilaton background corresponding to the SL(2, R)/U(1) model t
o its leading-order form (D = 2 black hole). As a consequence, there e
xists a ''scheme'' in which the string effective equations have the la
tter as an exact solution. However, the corresponding equation for the
tachyon (which, like other Weyl anomaly equations, has scheme-depende
nt form) still contains corrections of all orders in alpha'. As a resu
lt, the string ''probes'' still feel the alpha'-corrected background.
The field redefinitions we discuss contain the dilaton terms in the me
tric transformation law. We also comment on exact forms of the duality
transformation in different ''schemes''.