As neonatal chest images are frequently acquired to investigate the life-threatening lung diseases in prematurely born children, their optimisation in terms of X-ray exposure is required. The aim of this study was to investigate whether such dose-optimisation studies could be performed using a Monte Carlo computer model. More specifically, a Monte Carlo computer model was used to investigate the influence of Cu filtration on image quality and dose in neonatal chest imaging. Monte Carlo simulations were performed with the MCNPX code and used with voxel models representing prematurely born babies (590 and 1910 g). Physical image quality was derived from simulated images in terms of the signal difference-to-noise ratio and signal-to-noise ratio (SNR). To verify the simulation results, measurements were performed using the Gammex 610 Neonatal Chest Phantom, which represents a 1-2 kg neonate. A figure of merit was used to assist in evaluating the optimum balance between the image quality and the patient dose. The results show that the Monte Carlo computer model to investigate dose and image quality works well and can be used in dose-optimisation studies for real clinical practices. Furthermore, working at a specific constant incident air kerma (K(a,I)), additional filtration proved to increase SNR with 30 %, whereas working at a specific constant detector dose, extra Cu filtration reduces the lung dose with 25 %. Optimum balance between patient dose and image quality is found to be 60 kVp (using extra filtration).