We explain the arguments in support of the Berry-Robnik (1984 17 2413) picture of the energy-level statistics in the asymptotic strict (far) semiclassical limit of sufficiently small , where the entire energy spectrum can be represented as a statistically independent superposition of regular and irregular level sequences, the regular ones obeying the Poissonian statistics and the irregular ones the RMT statistics (GOE or GUE). We generalize the results to describe not only the level spacing distribution, the number variance and the delta statistics, but also arbitrary statistics (= the probability to find k levels inside an interval of length L - after unfolding). Very useful and effective approximations for are described. We demonstrate very clearly that this regime is excellently described by this picture for k as high as , the outer energy scale, even when taking into account the regular component and only one (the dominant) chaotic component. This we show numerically for the compactified standard map and for the quartic 2D billiard.