We present measurements of bounce harmonic Landau damping due to z-variations in the plasma potential, created by an azimuthally symmetric "squeeze" voltage Vs applied to the cylindrical wall. Traditional Landau damping on spatially uniform plasma is weak in regimes where the wave phase velocity v(ph) equivalent to w/k is large compared to the thermal velocity. However, z-variations in plasma density and potential create higher spatial harmonics, which enable resonant wave damping by particles with bounce-averaged velocities v(ph)/n, where n is an integer. In our geometry, the applied squeeze predominantly generates a resonance at v(ph)/3. Wave-coherent laser induced fluorescence measurements of particle velocities show a distinctive Landau damping signature at v(ph)/3, with amplitude proportional to the applied V-s. The measured (small amplitude) wave damping is then proportional to V-s(2), in quantitative agreement with theory over a range of 20 in temperature. Significant questions remain regarding "background" bounce harmonic damping due to ubiquitous confinement fields and regarding the saturation of this damping at large wave amplitudes. Published by AIP Publishing.