Let \( (R,m) \) be a one-dimensional local, reduced, noetherian ring. Assume that \(R\) is excellent with infinite residue field. Let \({\overline R}\) be the normalization of \(R\), \(C\) the conductor and \(t \) the type of \(R\). Consider the function \(\lambda^*(R)= t \lambda(R/C)-\lambda({\overline R}/R)\), where \(\lambda(\cdot)\) is the length function. Several authors have studied rings for which \(\lambda^*(R)=0,1 \) or \(\lambda^*(R)\leq t \). In this paper the authors consider the case \(\lambda^*(R)= t\) and describe possible values of \(\lambda(R/C+xR)\) and \(t\), where \(x\) is a minimal reduction of \(m\).