"Let $M$ be a hyperbolic $3$-manifold such that $partial M$ has at least two boundary tori $partial_0 M$ and partial_1 M$. Suppose that $M$ contains an essential orientable surface $P$ of genus $g$ with one outer boundary component $partial_0 P$, lying in $partial_0 M$ and having slope $lambda$ in $partial_0 M$, and $p$ inner boundary components $partial_i P$, $i = 1, cdots, p$, each having slope $alpha$ in $partial_1 M$. Let $eta$ be a slope in $partial_1 M$ and suppose that $M(eta)$ is toroidal. Let $hat T$ be a minimal essential torus in $M(eta)$, which means that $hat T$ is pierced a minimal number of times by the core of the ${eta}$-Dehn filling, among all essential tori in $M(eta)$. Let $T=hat T cap M$ and denote by $t$ the number of components of $partial T$. In this paper we prove: egin{itemize} item[(i)] If $t geq 3$, then $Delta (alpha, eta) leq 6+dfrac{10g-5}{p}$, item[(ii)] If $t=2$, then $Delta (alpha, eta) leq 13 +dfrac{24g-12}{p}$, item[(iii)] If $t=1$, then $Delta (alpha, eta) leq 1 $. end{itemize}"

Keywords: dehn filling, essential surface, toroidal manifold, scharlemann cycle