Accurate pore-pressure prediction is critical in hydrocarbon exploration and is especially important in the rapidly deposited Tertiary Baram Delta province where all economic fields exhibit overpressures, commonly of high magnitude and with narrow transition zones. A pore-pressure database was compiled using wireline formation interval tests, drillstem tests, and mud weights from 157 wells in 61 fields throughout Brunei. Overpressures are observed in 54 fields both in the inner-shelf deltaic sequences and in the underlying prodelta shales. Porosity vs. vertical effective stress plots from 31 fields reveal that overpressures are primarily generated by disequilibrium compaction in the prodelta shales but have been generated by fluid expansion in the inner-shelf deltaic sequences. However, the geology of Brunei precludes overpressures in the inner-shelf deltaics being generated by any conventional fluid expansion mechanism (e.g., kerogen-to-gas maturation), and we propose that these overpressures have been vertically transferred into reservoir units, via faults, from the prodelta shales. Sediments overpressured by disequilibrium compaction exhibit different physical properties to those overpressured by vertical transfer, and hence, different pore-pressure prediction strategies need to be applied in the prodelta shales and inner-shelf deltaic sequences. Sonic and density log data detect overpressures generated by disequilibrium compaction, and pore pressures are accurately predicted using an Eaton exponent of 3.0. Sonic log data detect vertically transferred overpressures even in the absence of a porosity anomaly, and pore pressures are reasonably predicted using an Eaton exponent of 6.5.