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 a 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.
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