  Nonlinearity and disorder are the recognized ingredients of the lattice
vibrational dynamics, the factors that could be diminished, but never excluded.
We generalize the concept of $q$-breathers -- periodic orbits in nonlinear
lattices, exponentially localized in the reciprocal linear mode space -- to the
case of weak disorder, taking the Fermi-Pasta-Ulan chain as an example. We
show, that these nonlinear vibrational modes remain exponentially localized
near the central mode and stable, provided the disorder is sufficiently small.
The instability threshold depends sensitively on a particular realization of
disorder and can be modified by specifically designed impurities. Basing on it,
an approach to controlling the energy flow between the modes is proposed. The
relevance to other model lattices and experimental miniature arrays is
discussed.
