Suppose M=V∪SW is a Heegaard splitting of M where V contains the only one essential disk DV in V and d(S)=n. Then, DV is separating and cuts V into two trivial compression bodies V1 and V2. Suppose F1 is a component of ∂−V such that F1=∂−V1 and S1=∂+V1∩S. Then, we can define ψF1:C(S)→C(F1). Suppose X is a full simplex of C(F1), HX is a handlebody obtained by attaching 2-handles to F1 along X and capping off possible 2-spheres by 3-handles. We denote V∪HX by VH. Then, MH=VH∪SHW is a Heegaard splitting of MH and MH is said to be a handlebody filling of M. In this paper, we suppose that 0<d(SH)<n, then there is a constant M such that either if 0<k≤M2 and 2k−2≤dC(F1)(D(HX),ψF1(DW))≤2k−1, then d(SH)=k or M2<d(SH)<n.