  We introduce orderings between total functions f,g: N -> N which refine the
pointwise "up to a constant" ordering <=cte and also insure that f(x) is often
much less thang(x). With such orderings, we prove a strong hierarchy theorem
for Kolmogorov complexities obtained with jump oracles and/or Max or Min of
partial recursive functions. We introduce a notion of second order conditional
Kolmogorov complexity which yields a uniform bound for the "up to a constant"
comparisons involved in the hierarchy theorem.
