  Kolmogorov suggested to measure quality of a statistical hypothesis $P$ for a
data $x$ by two parameters: Kolmogorov complexity $C(P)$ of the hypothesis and
the probability $P(x)$ of $x$ with respect to $P$.
  P. G\'acs, J. Tromp, P.M.B. Vit\'anyi discovered a small class of models that
are universal in the following sense. Each hypothesis $S_{ij}$ from that class
is identified by two integer parameters $i,j$ and for every data $x$ and for
each complexity level $\alpha$ there is a hypothesis $S_{ij}$ with $j\le i\le
l(x)$ of complexity at most $\alpha$ that has almost the best fit among all
hypotheses of complexity at most $\alpha$. The hypothesis $S_{ij}$ is
identified by $i$ and the leading $i-j$ bits of the binary representation of
the number of strings of complexity at most $i$. On the other hand, the initial
data $x$ might be completely irrelevant to the the number of strings of
complexity at most $i$. Thus $S_{ij}$ seems to have some information irrelevant
to the data, which undermines Kolmogorov's approach: the best hypotheses should
not have irrelevant information.
  To restrict the class of hypotheses for a data $x$ to those that have only
relevant information, Vereshchagin introduced a notion of a strong model for
$x$: those are models for $x$ whose total conditional complexity conditional to
$x$ is negligible. An object $x$ is called normal if for each complexity level
$\alpha$ at least one its best fitting model of that complexity is strong.
  In this paper we show that there are "many types" of normal strings. Our
second result states that there is a normal object $x$ such that all its best
fitting models $S_{ij}$ are not strong for $x$. Our last result states that
every best fit strong model for a normal object is again a normal object.
