Several authors have predicted a substantial excess noise factor K-p multiplying the quantum-limited Schawlow-Townes Linewidth for laser oscillators having nonorthogonal spatial modes, such as unstable-resonator lasers. Experimental observations of this factor have to date, however, been limited in both number and detail. We report here a detailed experimental measurement of this factor in a diode-pumped hard-edged unstable-resonator Nd:YVO4 laser. The measured excess noise factor K-p similar or equal to 330 is in reasonable agreement with the theoretically predicted value.