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As part of our effort to improve pore-pressure estimation in diagenetically altered mudstones, we have used wireline logs to estimate disequilibrium compaction and unloading contributions to the hard overpressure encountered in the Bekapai Field, Lower Kutai Basin. The maximum vertical effective stress that the overpressured mudstones have experienced is estimated from the density log using Dutta's relationship between vertical effective stress and void ratio. The sonic–density cross-plot is then used to estimate the sonic reference trend: that is, the expected sonic response if the mudstones were currently at maximum vertical effective stress. Finally, comparison of the sonic log with the sonic reference trend gives the unloading contribution to overpressure using Bowers’ unloading relationship between the vertical effective stress and velocity. In spite of poor data quality, fair results were obtained showing a steady increase in disequilibrium compaction overpressure below the top of the sharp pressure ramp. Immediately below the pressure ramp, the unloading contribution to overpressure dominates, with gas generation being the most likely cause. Our interpretation explains the pressure and wireline log data in this deltaic setting satisfactorily, resolving a debate on overpressure-generation mechanisms in the shelfal area of the basin that has been ongoing for 25 years.