  It is impossible to effectively modify a string in order to increase its
Kolmogorov complexity. But is it possible to construct a few strings, not
longer than the input string, so that most of them have larger complexity? We
show that the answer is yes. We present an algorithm that on input a string $x$
of length $n$ returns a list with $O(n^2)$ many strings, all of length $n$,
such that 99\% of them are more complex than $x$, provided the complexity of
$x$ is less than $n - \log \log n - O(1)$. We obtain similar results for other
parameters, including a polynomial-time construction.
