  As is well known, the Lefschetz theorems for the \'etale fundamental group of
SGA1 do not hold. We fill a small gap in the literature showing they do for
tame coverings. Let $X$ be a regular projective variety over a field $k$, and
let $D\hookrightarrow X$ be a strict normal crossings divisor. Then, if $Y$ is
an ample regular hyperplane intersecting $D$ transversally, the restriction
functor from tame \'etale coverings of $X\setminus D$ to those of $Y\setminus
D\cap Y$ is an equivalence if dimension $X \ge 3$, and fully faithful if
dimension $X=2$. The method is dictated by Grothendieck-Murre ("The tame
fundamental group of a formal neighbourhood of a divisor with normal crossings
on a scheme", Springer LNM 208). The authors showed that one can lift tame
coverings from $Y\setminus D\cap Y$ to the complement of $D\cap Y$ in the
formal completion of $X$ along $Y$. One has then to further lift to $X\setminus
D$.
