  Three magnon bound states in all total spin sectors of general nonintegrable
exactly rung-dimerized spin ladder are obtained by Bethe Ansatz. Basing on this
result a dispersion law for $m$-magnon ($m>3$) bound states is conjectured. It
is suggested that (depending on correlations between coupling constants) a
behavior of the gas parameter (density of rung-triplets) on the boundary of the
rung-dimerized phase may either be smooth or have a leap.
