We determine to what extent low-temperature thermochronology data, in particular from age-elevation profiles, provide independent and quantitative estimates on denudation rates and relief development. Thermochronological age-elevation profiles have been widely used to infer exhumation histories. However, their interpretation has remained inherently one-dimensional, neglecting potential effects of lateral offsets between samples. Furthermore, the potential effects of transient topography on crustal isotherms and consequently on thermochronological data have not yet been addressed in detail. We investigate this problem with the aim of deriving independent estimates of both denudation rates and relief history from low-temperature thermochronometers, measuring the relative uncertainties on these parameters and finally constraining the timing of potential variations in denudation rate and/or relief development. We adopt a non-linear inversion method combining the three-dimensional thermal-kinematic model Pecube, which predicts thermal histories and thermochronological ages from an input denudation and relief history, with an inversion scheme based on the Neighbourhood Algorithm. We use synthetic data predicted from imposed denudation and relief histories and quantitatively assess the resolution of thermochronological data collected along an age-elevation profile. Our results show that apatite fission-track (AFT) ages alone do not provide sufficient quantitative information to independently constrain denudation and relief histories. Multiple thermochronometers (apatite (U-Th)/He (AHe) ages and/or track-length measurements combined with AFT ages) are generally successful in constraining denudation rates and timing of rate changes, the optimum combination of thermochronometers varying with the input scenario (relief change or varying denudation rates). However, relief changes can only be quantified and precisely constrained from thermochronological age-elevation profiles if the rate of relief growth is at least 2-3 times higher than the background denudation rate. This limited resolution is due to the depth of the closure isotherm (between ˜ 70 and 110 °C) for the AFT and AHe systems, which only partly record topographic change. New thermochronometers (such as 4He/3He or OSL) that are sensitive to lower temperatures may be the key for resolving this issue.