  We introduce a concept of the bounded rank (with respect to a positive
constant) for unital C*-algebras as a modification of the usual real rank and
present a series of conditions insuring that bounded and real ranks coincide.
These observations are then used to prove that for a given $n$ and $K > 0$
there exists a separable unital C*-algebra $Z_{n}^{K}$ such that every other
separable unital C*-algebra of bounded rank with respect to $K$ at most $n$ is
a quotient of $Z_{n}^{K}$.
