  We focus on inducing topological state from regular, or irregular scattering
in (i) p-wave superconducting wires and (ii) Rashba wires proximity coupled to
an s-wave superconductor. We find that contrary to common expectations the
topological properties of both systems are fundamentally different: In p-wave
wires, disorder generally has a detrimental effect on the topological order and
the topological state is destroyed beyond a critical disorder strength. In
contrast, in Rashba wires, which are relevant for recent experiments, disorder
can {\it induce} topological order, reducing the need for quasiballistic
samples to obtain Majorana fermions. Moreover, we find that the total phase
space area of the topological state is conserved for long disordered Rashba
wires, and can even be increased in an appropriately engineered superlattice
potential.
