  We are developing a covariant model for all mesons that can be described as
quark-antiquark bound states in the framework of the Covariant Spectator Theory
(CST) in Minkowski space. The kernel of the bound-state equation contains a
relativistic generalization of a linear confining potential which is singular
in momentum space and makes its numerical solution more difficult. The same
type of singularity is present in the momentum-space Schr\"odinger equation,
which is obtained in the nonrelativistic limit. We present an alternative,
singularity-free form of the momentum-space Schr\"odinger equation which is
much easier to solve numerically and which yields accurate and stable results.
The same method will be applied to the numerical solution of the CST
bound-state equations.
