The phonon spectrum of solid deuterium has been measured using coherent inelastically-scattered thermal neutrons. Measurements were conducted at pressures up to 4.5 kbar with a temperature range between 4 and 50 K. Force constants of a harmonic model were calculated from the phonon energies at two molar volumes, 15.87 and 14.4 cm3/mole. Most bulk thermodynamic properties calculated from the force constants are in good agreement with directly measured values. The temperature variations of phonon energy shifts and linewidth increases were measured. Phonon linewidths were determined by deconvolution of the spectra assuming a Gaussian instrument-resolution function and a Lorentzian natural line shape. Mode Grüneisen parameters were measured and lie between 1.8 and 2.2. The basal longitudinal modes show the largest shifts in energy with compression.