  Let $V_{t}$ be a driftless subordinator, and let denote $m_{t}^{(1)} \geq
m_{t}^{(2)} \geq\ldots$ its jump sequence on interval $[0,t]$. Put $V_{t}^{(k)}
= V_{t} - m_{t}^{(1)} - \ldots- m_{t}^{(k)}$ for the $k$-trimmed subordinator.
In this note we characterize under what conditions the limiting distribution of
the ratios $V_{t}^{(k)} / m_{t}^{(k+1)}$ and $m_{t}^{(k+1)} / m_{t}^{(k)}$
exist, as $t \downarrow0$ or $t \to\infty$.
