Shannon entropy for lower position and momentum eigenstates of Pöschl - Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density ρ(x) moves right when the potential parameter V1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter |V2|. Concerning the momentum information entropy density ρ(p), we observe that its amplitude increases with increasing potential parameter V1, but its amplitude decreases with increasing |V2|. The Bialynicki - Birula - Mycielski (BBM) inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V1, but decreases with |V2|. However, the variation of momentum information entropy is contrary to that of the position information entropy. © 2013 Chinese Physical Society and IOP Publishing Ltd.