  We show that for the voter model on $\{0,1\}^{\mathbb{Z}}$ corresponding to a
random walk with kernel $p(\cdot)$ and starting from unanimity to the right and
opposing unanimity to the left, a tight interface between 0's and 1's exists if
$p(\cdot)$ has finite second moment but does not if $p(\cdot)$ fails to have
finite moment of order $\alpha$ for some $\alpha <2$.
