Anisotropy of magnetic susceptibility data obtained from discrete sub-samples recovered from two Integrated Ocean Drilling Program sites (Expedition 347 sites M0061 and M0062 in the Baltic Sea) by an Advanced Piston Corer are compared to results obtained on sub-samples recovered by replicate 6 m long Kullenberg piston cores. Characteristic natural remanence directions were obtained from the total of 1097 sub-samples using principal component analyses. The three principal anisotropy axes of sub-samples taken from Advanced Piston Core liners align to the sub-sample axes, with the maximum axis (K1) parallel to the split core surfaces, possibly caused by outwards relaxation of the core-liners after splitting. A second anomalous anisotropy fabric is characterized by steep values of the angular difference between the inclination of the minimum anisotropy axes (K3) and that expected for horizontal bedding (90°). This fabric is confined to the upper 1–2 m of the Kullenberg cores and specific sections of the advanced piston cores, and we attribute it to conical deformation caused by either excessive penetration speeds and downwards dragging of sediment along the edge of the liner or stretching caused by undersampling. By using our data in an example, we present a protocol to accept palaeomagnetic secular variation data that uses (i) a threshold 90-K3 value of 15°, combined with a modelled, locally applicable minimum inclination of 65° and (ii) an A95 cone of confidence based on Fisher statistics applied to virtual geomagnetic pole distributions.