The generalized pseudospectral method is used to study the bound-state spectra of some of the exponentially screened Coulomb potentials, namely, the exponential cosine screened Coulomb (ECSC) and general exponential screened Coulomb (GESC) potential, with special emphasis on higher states and stronger interaction. Eigenvalues accurate up to 11 significant figures are obtained through a nonuniform optimal spatial discretization of the radial Schrödinger equation. All the 55 eigenstates of ECSC potential with n ≤ 10 and 36 eigenstates of GESC potential with n ≤ 8 are considered for arbitrary values of the screening parameter, covering a wide range of interaction. Excited states as high as up to n = 18 have been computed with high accuracy for the first time. Excellent agreement with the literature data has been observed in all cases. All the GESC eigenstates are calculated with much greater accuracy than the existing methods available in literature. Many l ≠ 0 states of this potential are reported here. In both cases, a detailed variation of energies with respect to the parameters in potential is monitored. © 2012 Wiley Periodicals, Inc.