  The size $b$ of the smallest bidirectional macro scheme, which is arguably
the most general copy-paste scheme to generate a given sequence, is considered
to be the strictest reachable measure of repetitiveness. It is strictly
lower-bounded by measures like $\gamma$ and $\delta$, which are known or
believed to be unreachable and to capture the entropy of repetitiveness. In
this paper we study another sequence generation mechanism, namely compositions
of a morphism. We show that these form another plausible mechanism to
characterize repetitive sequences and define NU-systems, which combine such a
mechanism with macro schemes. We show that the size $\nu \leq b$ of the
smallest NU-system is reachable and can be $o(\delta)$ for some string
families, thereby implying that the limit of compressibility of repetitive
sequences can be even smaller than previously thought. We also derive several
other results characterizing $\nu$.
