A discrete subset of
C
n
\mathbb C^n
is said to be tame if there is an automorphism of
C
n
\mathbb C^n
taking the given discrete subset to a subset of a complex line; such tame sets are known to allow interpolation by automorphisms. We give here a fairly general sufficient condition for a discrete set to be tame. In a related direction, we show that for certain discrete sets in
C
n
\mathbb C^n
there is an injective holomorphic map from
C
n
\mathbb C^n
into itself whose image avoids an
ϵ
\epsilon
-neighborhood of the discrete set. Among other things, this is used to show that, given any complex
n
n
-torus and any finite set in this torus, there exist an open set containing the finite set and a locally biholomorphic map from
C
n
\mathbb C^n
into the complement of this open set.