Mechanisms of acoustic energy dissipation in heterogeneous solids attract much attention in view of their importance for material characterization, nondestructive testing, and geophysics. Due to the progress in measurement techniques in recent years it has been revealed that rocks can demonstrate extremely high strain sensitivity of seismo-acoustic loss. In particular, it has been found that strains of order 10^-8 produced by lunar and solar tides are capable to cause variations in the

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... ustic decrement on the order of several percents. Some laboratory data (although obtained for higher frequencies) also indicate the presence of very high dissipative nonlinearity. Conventionally discussed dissipation mechanisms (thermoelastic loss in dry solids, Biot and squirt-type loss in fluid-saturated ones) do not suffice to interpret such data. Here, the dissipation at individual cracks is revised taking into account the influence of wavy asperities of their surfaces quite typical of real cracks, which can drastically change the values of the relaxation frequencies and can result in giant strain sensitivity of the dissipation without the necessity to assume the presence of unrealistically thin (and, therefore, unrealistically soft) cracks. In particular, these mechanisms suggest interpretation for observations of pronounced amplitude modulation of seismo-acoustic waves by tidal strains.