The use of T-rays, or terahertz radiation, to identify substances by their spectroscopic fingerprints is a rapidly moving field. The dominant approach is presently terahertz timedomain spectroscopy. However, a key problem is that ambient water vapour is ubiquitous and the consequent water absorption distorts the T-ray pulses. Water molecules in the gas phase selectively absorb incident T-rays at discrete frequencies corresponding to their molecular rotational transitions. When T-rays propagate through an atmosphere, this results in prominent resonances spread over the T-ray spectrum; furthermore, in the time domain, fluctuations after the main pulse are observed in the T-ray signal. These effects are generally undesired, since they may mask critical spectroscopic data. So, ambient water vapour is commonly removed from the T-ray path by using a closed chamber during the measurement. Yet, in some applications, a closed chamber is not always feasible. This situation, therefore, motivates the need for an optional alternative method for reducing these unwanted artefacts. This paper represents a study on a computational means that is a step towards addressing the problem arising from water vapour absorption over a moderate propagation distance. Initially, the complex frequency response of water vapour is modelled from a spectroscopic catalogue. Using a deconvolution technique, together with fine tuning of the strength of each resonance, parts of the water vapour response are removed from a measured T-ray signal, with minimal signal distortion, thus providing experimental validation of the technique.