Single molecules of tetra-tert-butylterrylene were investigated by fluorescence excitation spectroscopy in thin spin-coated films of poly(isobutylene). These are the first single molecule experiments in a truly amorphous host. We recorded the spectra of many different single molecules and found a broad distribution of line widths giving evidence of the wide variety of locally varying dynamics seen by the probe chromophores. We also investigated spectral diffusion using the fluorescence correlation technique. We present a specific example where the shape of the fluorescence autocorrelation function decaying due to spectral diffusion changes with increasing excitation intensity. The results are also compared to similar investigations with tetra-tert-butylterrylene in a polyethylene matrix.