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Let $R$ be a one-dimensional, local, Noetherian domain, $\R$ the integralclosure of $R$ in its quotient field and $v(R)$ the value set defined by theusual valuation.  The aim of the paper is to study the non-negative invariant $b:=(c-\delta)r-\delta $, where $c, \delta, r$ denote the conductor, the length of $\R/R$ andthe Cohen Macaulay type, respectively. In particular, the classification of thesemigroups $v(R)$ for rings having $b\leq 2(r-1)$ is realized. This method ofclassification might be successfully utilized with similar arguments but moreboring computations in the cases $b\leq q(r-1), $ for reasonably low values of$q$. The main tools are type sequences and the invariant $k$ which estimatesthe number of elements in $v(R)$ belonging to the interval $[c-e,c), e$ beingthe multiplicity of $R$.

A classification of one-dimensional local domains based on the invariant $(c-\delta)r-\delta$