A method of determining variations in wall thickness in an elongate, cylindrical, hollow, ferromagnetic tube defining a tube wall, comprising the steps of: a) energizing the tube with an at least longitudinally extending magnetic field generated inside the tube that gives rise to near- or over-saturation of the tube wall material; b) using a magnetic field-detecting logging tool (28, 28') to (i) detect two or more magnetic flux leakage signals generated inside the tube other than in the material of the tube wall, resulting from such energizing, at plural circumferential locations on the inner and/or outer surfaces of the tube and at a plurality of distances along the tube and (ii) generate two or more magnetic flux leakage data signals indicative thereof; c) iteratively, one or more times, using a model of the relationship between the two or more magnetic flux leakage data signals generated in Step b) and the thickness of the tube wall to derive the thickness profile of the tube wall by relating a defect-free flux parameter representing a field strength defect offset in a magnetization plot of the tube averaged across two or more sensors (44, 46) of the logging tool and a maximum flux response within the defect measured by the logging tool to give rise to a first approximation ratio, forming part of the model, that is proportional to defect penetration, said iteration including: d) inverting in accordance with the model to produce a defect profile which depends on the magnetic flux leakage signals without any external parameters; e) determining the defect penetration by determining the maximum of the defect profile; and f) generating one or more signals representing a wall thickness profile based on the defect penetration. a) energizing the tube with an at least longitudinally extending magnetic field generated inside the tube that gives rise to near- or over-saturation of the tube wall material; b) using a magnetic field-detecting logging tool (28, 28') to (i) detect two or more magnetic flux leakage signals generated inside the tube other than in the material of the tube wall, resulting from such energizing, at plural circumferential locations on the inner and/or outer surfaces of the tube and at a plurality of distances along the tube and (ii) generate two or more magnetic flux leakage data signals indicative thereof; c) iteratively, one or more times, using a model of the relationship between the two or more magnetic flux leakage data signals generated in Step b) and the thickness of the tube wall to derive the thickness profile of the tube wall by relating a defect-free flux parameter representing a field strength defect offset in a magnetization plot of the tube averaged across two or more sensors (44, 46) of the logging tool and a maximum flux response within the defect measured by the logging tool to give rise to a first approximation ratio, forming part of the model, that is proportional to defect penetration, said iteration including: d) inverting in accordance with the model to produce a defect profile which depends on the magnetic flux leakage signals without any external parameters; e) determining the defect penetration by determining the maximum of the defect profile; and f) generating one or more signals representing a wall thickness profile based on the defect penetration.