The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation and chiral-conjugation transformations are discussed and it is shown that a finite set of intrinsically relativistic bound-state solutions appears as poles of the transmission amplitude. It is also shown that those bound solutions disappear asymptotically as one approaches the conditions for the realization of the so-called spin and pseudospin symmetries in a four-dimensional space-time. (C) 2014 Elsevier Inc. All rights reserved.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)UNESP, Dept Quim & Fis, BR-12516410 Guaratingueta, SP, BrazilUNESP, Dept Quim & Fis, BR-12516410 Guaratingueta, SP, BrazilCNPq: 305201/2012-3