  We consider the problem of determining the monic integer transfinite diameter
for real intervals $I$ of length less than 4. We show that $t_M([0,x])$, as a
function in $x>0$, is continuous, therefore disproving two conjectures due to
Hare and Smyth. Consequently, for $n>2\in\naturals$, we define the quantity
$b_{\max}(n)&=&\sup_{b>\frac{1}{n}}\left\{b|t_M([0,b])=\tfrac{1}{n}\right.\right\}$
and give lower and upper bounds of $b_{\max}(n)$. Finally, we improve the lower
bound for $b_{\max}(n)$ for $3\leq n\leq 8$.
