An optimal algorithm, which suitably combines two dosemeter readings, one dosemeter on the chest and the other on the back, for better estimation of effective dose equivalent (HE) and effective dose (E), was developed by utilising hundreds of broad parallel photon beam irradiation geometries. The developed algorithm, weighting front (chest) and back dosemeter readings by 0.58 and 0.42, respectively, was found to be superior to other currently available algorithms, neither underestimating HE or E by more than 14%, nor overestimating by more than a few tens of a per cent for a broad range of frontal and dorsal incident beams. Like other algorithms, however, this algorithm tends to overestimate HE and E significantly for the lateral, overhead and underfoot beam directions. This study also suggests that this overestimation problem significantly decreases when one uses typical commercial dosemeters instead of isotropic-responding dosemeters.