In a graph $G$ of maximum degree $\Delta$ let $\gamma$ denote the largest fraction of edges that can be $\Delta$ edge-coloured. Albertson and Haas showed that $\gamma \geq \frac{13}{15}$ when $G$ is cubic \cite{AlbHaa}. The notion of $\delta-$minimum edge colouring was introduced in \cite{FouPhd} in order to extend the so called {\em parcimonious edge-colouring} to graphs with maximum degree $3$. We propose here an english translation of some structural properties already present in \cite{Fou,FouPhd} (in French) for $\delta-$minimum edge colourings of graphs with maximum degree $3$.