Bifacial solar cells have received considerable attention due to the potential to achieve higher energy yield compared to monofacial cells. However, in bifacial cells, p(+)-Si layers are usually produced by boron diffusion, which makes such cells more expensive compared to monofacial cells with a full-area screen-printed Al-alloyed Al-p(+) back-surface-field (BSF). Recently, we have demonstrated proof-of-concept that bifacial cells, which, in addition, are also suitable for application in low-concentration systems (3-6 suns), can be produced from commercially available, standard monofacial SiN/(n(+)pp(+))Cz-Si/Al structures with full-area Al-p(+)-BSF. For this purpose, the residual Al paste was removed and a number of solar cells were prepared differing in the sheet resistance of the Al-p(+)-BSF (Rp+), which was varied from 14 Omega/sq to 123 Omega/sq by thinning the Al-p(+) layer using one-sided etch-back process. Thinning of the Al-p(+)-BSF significantly improved the efficiency under 1-sun front/rear-side illumination: from 16.0%/7.5% (at Rp+ = 14 Omega/sq) to 17.5%/11.2% (at Rp+ = 81 Omega/sq). The equivalent efficiency at 1-sun front illumination and 20/50% albedo of 1-sun illumination increased from 17.7%/20.1% (at Rp+ = 14 Omega/sq) to 19.9%/23.5% (at Rp+ = 81 Omega/sq). In this paper, we present the results of systematic study of the developed bifacial cells. Thinning-induced changes in the properties of the cells are analyzed in detail. The critical aspects which might explain the performance of the developed cells are addressed. In addition, bifacial cells are compared with standard monofacial cells fabricated using the precursor of the same batch.