Beam hardening filters have long been employed in X-ray Computed Tomography (CT) to preferentially absorb soft and low-energy X-rays having no or little contribution to image formation, thus allowing the reduction of patient dose and beam hardening artefacts. In this work, we studied the influence of additional copper (Cu) and aluminium (Al) flat filters on patient dose and image quality and seek an optimum filter thickness for the GE LightSpeed VCT 64-slice CT scanner using experimental phantom measurements. Different thicknesses of Cu and Al filters (0.5-1.6mm Cu, 0.5-4mm Al) were installed on the scanner's collimator. A planar phantom consisting of 13 slabs of Cu having different thicknesses was designed and scanned to assess the impact of beam filtration on contrast in the intensity domain (CT detector's output). To assess image contrast and image noise, a cylindrical phantom consisting of a polyethylene cylinder having 16 holes filled with different concentrations of K2HPO4 solution mimicking different tissue types was used. The GE performance and the standard head CT dose index (CTDI) phantoms were also used to assess image resolution characterized by the modulation transfer function (MTF) and patient dose defined by the weighted CTDI. A 100mm pencil ionization chamber was used for CTDI measurement. Finally, an optimum filter thickness was determined from an objective figure of merit (FOM) metric. The results show that the contrast is somewhat compromised with filter thickness in both the planar and cylindrical phantoms. The contrast of the K2HPO4 solutions in the cylindrical phantom was degraded by up to 10% for a 0.68mm Cu filter and 6% for a 4.14mm Al filter. It was shown that additional filters increase image noise which impaired the detectability of low density K2HPO4 solutions. It was found that with a 0.48mm Cu filter the 50% MTF value is shifted by about 0.77lp/cm compared to the case where the filter is not used. An added Cu filter with approximately 0.5mm thickness accounts for 50% reduction in radiation-absorbed dose as measured by the weighted CTDI. The FOM results indicate that with an additional filter of 0.5mm Cu or minimum 4mm Al, a good compromise between image quality and patient dose is achieved for CT images acquired at tube voltages of 120 and 140kVp. The results seem to indicate that an optimum filter for high kVp acquisitions, routinely used in cardiovascular imaging, should be 0.5mm copper or 4mm aluminium minimum.