Fluorescence excitation spectroscopy of single chromophores in an amorphous polymer at low temperatures allows the study of single two-level systems (TLSs) of the matrix. With increasing temperature, more TLSs are thermally activated and contribute to random flipping, splitting, and/or broadening of single-molecule lines. In this paper we report on temperature-dependent changes of the intensity ratio between different components of single-molecule lines. The system under study is tetra-tert-butyl-terrylene in poly-isobutylene. Since the temperature dependent changes are due to thermal activation of individual TLSs, we could calculate the asymmetry of several of these TLSs yielding values between 0.25 and 1.5 meV. Some of the TLSs do not follow the Boltzmann activation law. (C) 2003 American Institute of Physics.