  The irreducible representations of the Witt algebra $W$ are completely known.
A classification of the irreducible $U_\chi(W)$--modules was first established
by Chang and later simplified by Strade. The aim of this article is to give a
classification of the extensions of the simple $U_\chi(W)$--modules having
$p$--character $\chi$ of height $-1,0,1$ and $p-1$ where $p$ denotes the
characteristic of the ground field.
