As lead sulfide is an important semiconductor, it is of great interest to identify possible (meta)stable modifications, both at standard and elevated pressures. To predict such structures, global optimizations on the energy landscape of PbS were performed for several pressures, using simulated annealing followed by local optimization of the candidates found. In order to be able to take the effect of the nonbonding valence electrons of Pb into account, ab initio energies were employed for both the global and local optimization. Besides the experimentally known modifications (NaCl structure type at standard pressure and the CsCl structure type at high pressure), several additional promising structures, which might be accessible synthetically, were found; exhibiting, e.g., the TlI type (Cmcm), the FeB type (Pnma), and the \ensuremath{\alpha}-GeTe type ($R$3$m$).