  We discuss the effect of weak bond-disorder in two-leg spin ladders on the
dispersion relation of the elementary triplet excitations with a particular
focus on the appearance of bound states in the spin gap. Both the cases of
modified exchange couplings on the rungs and the legs of the ladder are
analyzed. Based on a projection on the single-triplet subspace, the
single-impurity and small cluster problems are treated analytically in the
strong-coupling limit. Numerically, we study the problem of a single impurity
in a spin ladder by exact diagonalization to obtain the low-lying excitations.
At finite concentrations and to leading order in the inter-rung coupling, we
compare the spectra obtained from numerical diagonalization of large systems
within the single-triplet subspace with the results of diagrammatic techniques,
namely low-concentration and coherent-potential approximations. The
contribution of small impurity clusters to the density of states is also
discussed.
