  We consider finite systems of contractive homeomorphisms of a complete metric
space, which are non-redundant on every level. In general this separation
condition is weaker than the strong open set condition and is not equivalent to
the weak separation property. We prove that this separation condition is
equivalent to the strong Markov property (see definition below). We also show
that the set of $N$-tuples of contractive homeomorphisms, which are
non-redundant on every level, is a $G_\delta$ set in the topology of pointwise
convergence of every component mapping with an additional requirement that the
supremum of contraction coefficients of mappings be strictly less than one. We
give several sufficient conditions for this separation property. For every
fixed $N$-tuple of $d\times d$ invertible contraction matrices from a certain
class, we obtain density results for $N$-tuples of fixed points which define
$N$-tuples of mappings non-redundant on every level.
