$p-Hitting-Set ≤fpt p-WD_hs$. On the word of $(P, k)$ the reduction writes, when $k ≤ n$, the structure of the compressed instance (universe: the first occurrences of the members plus $min k m$ spare elements, then one element per set; $VERT$, $EDGE$ and the incidence relation $I$) with weight $min k m$, and a fixed no-instance when $k > n$; the witnesses of $hs(X)$ of that weight are the hitting sets of that size, and compression keeps the answer. The new parameter is at most $k + 1$, and an IMP+ program computes the reduction within $100000 (|x| + 1)^3$ steps.