  Over a connected geometrically unibranch scheme $X$ of finite type over a
finite field, we show finiteness of the number of irreducible $\bar
\Q_\ell$-lisse sheaves, with bounded rank and bounded ramification in the sense
of Drinfeld, up to twist by a character of the finite field. On $X$ smooth,
with bounded ramification in the sense of bounding the Swan conductors on
curves, this is Deligne's theorem. Version 2: We prove also that for Deligne's
finiteness theorem, it is enough to assume $X$ normal. However, the proof uses
the smooth case, unlike the proof in the case of bounded ramification in the
sense of Drinfeld. Finally we discuss the various notions of boundedness of
ramification used.
