  Based on a three-potential formalism we propose mathematically well-behaved
Faddeev-type integral equations for the atomic three-body problem and descibe
their solutions in Coulomb-Sturmian space representation. Although the system
contains only long-range Coulomb interactions these equations allow us to reach
solution by approximating only some auxiliary short-range type potentials. We
outline the method for bound states and demonstrate its power in benchmark
calculations. We can report a fast convergence in angular momentum channels.
