Broadband dielectric spectroscopy is employed to investigate the non-Debye relaxation behavior in a dendrimeric alkyd resin. From temperature-dependent measurements at ambient pressure, we found a very broad distribution of relaxation times. This is attributed to the complex geometrical topology of the molecule. However, compression significantly reduces the non-Debye character of the dielectric response; thus, pressure induces dynamic homogeneity in the dendrimeric alkyd resin.