We predict the occurrence of large ferroelectric polarization and piezoelectricity in the hypothetical perovskite-structure oxides, bismuth aluminate (BiAlO3) and bismuth gallate (BiGaO3), using density functional theory within the local density approximation. We show that BiGaO3 will have a similar structure to PbTiO3, although with much stronger tetragonal distortion and therefore improved ferroelectric properties. Likewise, BiAlO3 shares structural characteristics with antiferrodistortive PbZrO3, but it is also a ferroelectric with large polarization. Therefore, we propose the Bi(Al,Ga)O3 system as a replacement for the widely used piezoelectric material, Pb(Zr,Ti)O3 (PZT), that will avoid the environmental toxicity problems of lead-based compounds. Finally, we show that, in both BiAlO3 and BiGaO3, the large distortions from the prototypical cubic structure are driven by the stereochemical activity of the Bi lone pair.