  Given a valuation $v$ with quotient field $K$ and a sequence $\mathcal{K}
:K_0\subseteq K_1\subseteq\cdots$ of finite extensions of $K$, we construct a
weighted tree $\mathcal{T}(v,\mathcal{K})$ encoding information about the
ramification of $v$ in the extensions $K_i$; conversely, we show that a
weighted tree $\mathcal{T}$ can be expressed as $\mathcal{T}(v,\mathcal{K})$
under some mild hypothesis on $v$ or on $\mathcal{T}$. We use this construction
to construct, for every countable successor ordinal number $\alpha$, an almost
Dedekind domain $D$, integral over $V$ (the valuation domain of $v$) whose
SP-rank is $\alpha$. Subsequently, we extend this result to countable limit
ordinal numbers by considering integral extensions of Dedekind domains with
countably many maximal ideals.
