X-ray mammography is the gold standard technique in breast cancer screening programmes. One of the main challenges that mammography is still facing is scattered radiation, which degrades the quality of the image and complicates the diagnosis process. Anti-scatter grids, the main standard physical scattering reduction technique, have some unresolved challenges as they increase the dose delivered to the patient, do not remove all the scattered radiation and increase the cost of the equipment. Alternative scattering reduction methods based on post-processing algorithms, have lately been under investigation. This study is concerned with the use of image post-processing to reduce the scatter contribution in the image, by convolving the primary plus scatter image with kernels obtained from simplified Monte Carlo simulations. The proposed semi-empirical approach uses up to five thickness-dependant symmetric kernels to accurately estimate the scatter contribution of different areas of the image. Single breast thickness-dependant kernels can over-estimate the scatter signal up to 60 %, while kernels adapting to local variations have to be modified for each specific case adding high computational costs. The proposed method reduces the uncertainty to a 4-10 % range for a 35-70 mm breast thickness range, making it a very efficient, case-independent scatter modelling technique. To test the robustness of the method, the scattered corrected image has been successfully compared against full Monte Carlo simulations for a range of breast thicknesses. In addition, clinical images of the 010A CIRS phantom were acquired with a mammography system with and without the presence of the anti-scatter grid. The grid-less images were post-processed and their quality was compared against the grid images, by evaluating the contrast-to-noise ratio and variance ratio using several test objects, which simulate calcifications and tumour masses. The results obtained show that the method reduces the scatter to similar levels than the anti-scatter grids.