We prove that for prime $p$, $p\to +\infty$, integer $r\geqslant 4$ and $q = p^{r}$ an incomplete Kloosterman sum of length $N$ to modulus $q$ can be estimated non-trivially (with power-saving factor) for very small $N$, namely, for $N\gg (q\log{q})^{1/(r-1)}$.