  We consider Sinai's walk in i.i.d. random scenery and focus our attention on
a conjecture of R\'ev\'esz \cite{r05} concerning the upper limits of Sinai's
walk in random scenery when the scenery is bounded from above. A close study of
the competition between the concentration property for Sinai's walk and
negative values for the scenery enables us to prove that the conjecture is true
if the scenery has "thin" negative tails and is false otherwise.
