  Transport properties of narrow two-dimensional conducting wires in which the
electron scattering is caused by side edges' roughness have been studied. The
method for calculating dynamic characteristics of such conductors is proposed
which is based on the two-scale representation of the mode wave functions at
weak scattering. With this method, fundamentally different {\it by-height} and
{\it by-slope} scattering mechanisms associated with edge roughness are
discriminated. The results for single-mode systems, previously obtained by
conventional methods, are proven to correspond to the former mechanism only.
Yet the commonly ignored by-slope scattering is more likely dominant. The
electron extinction lengths relevant to this scattering differ substantially in
functional structure from those pertinent to the by-height scattering. The
transmittance of ultra-quantum wires is calculated over all range of scattering
parameters, from ballistic to localized transport of quasi-particles. The
obtained dependence of scattering lengths on the disorder parameters is valid
qualitatively for arbitrary inter-correlation of the boundaries' defects.
