Abstract A new class of one-term separable potentials for cluster-cluster (d, t, α) scattering is proposed. The analytical form of the potential form factors for the proposed potentials is obtained directly from the cluster representation of the shell-model wave functions with the corresponding shell-model parameters, and thus a single analytical expression is taken for all (essential) partial waves for the given pair of nuclei. In particular, the S-, D- and G-scattering phases in the 4 He- 4 He system and the S-phase for 4 He-d scattering have been investigated. A quite adequate description of the phase shifts and radial wave functions in the continuum is obtained. This is due to the fact that in the systems concerned only one (quasi)-stationary state predominates in a given scattering channel. A very simple general relation connecting the positions of the zeros of the phase shifts and the zeros of the oscillator Laguerre polynomials in the momentum representation valid for different partial waves and different cluster pairs is given. Application of the proposed potentials to other two- and three-cluster systems is discussed.