Let $r\ge 3$. For an $r$-uniform hypergraph $G$ let $\tau (G)$ denote the covering number (or transversal number), the minimum size of a set of vertices which includes at least one from each edge in $G$.Determine the best possible $t$ such that, if $G$ is an $r$-uniform hypergraph $G$ where every subgraph $G^{\prime }$ on at most $3r-3$ vertices has $\tau (G^{\prime })\le 1$, we have $\tau (G)\le t$.