  Lifetime differences of heavy hadrons can be consistently computed in
heavy-quark expansion. The leading effects appear through spectator
interactions at order 1/m_b^3. We compute a well-defined subset of 1/m_b^4
corrections to the lifetime ratio of Lambda_b baryon and B_d meson. We find
that these corrections are large and should be taken into account in the
systematic analysis of heavy hadron lifetimes. We claim that they could shift
the ratio \tau_{\Lambda_b}/\tau_{B_d} by as much as -4.5%, significantly
reducing the discrepancy between the theoretical predictions and experimental
observations.
