In this paper the phenomenon of the ultrafast relaxation of a system coupled to a small bath is treated. The system, representing the pyrazine molecule, contains 4 vibrational modes and 2 electronic states coupled via a conical intersection, and the bath is a set of up to 20 harmonic oscillators. The dynamics of the complete system are described by wave packet propagation using the multiconfiguration time-dependent Hartree method. By the use of multidimensional single-particle functions it was possible to obtain results of a high quality, even for the complete system with 24 degrees of freedom. The full wave function for the system and bath are analyzed to reveal the characteristics of the system-bath interaction, such as energy transfer to the bath, or the effect of the bath on the state populations. The results show that the damping due to the bath model adopted is not only nonhomogeneous but also selective : certain high frequencies are found to remain at long times.