Seismic observations of the Earth’s inner-core testify to it being both a complex and dynamic part of the Earth. It exhibits significant variation in seismic attenuation and velocity with position, depth and direction. Interpretation of which is difficult without knowledge of the anelastic processes active in the inner-core is difficult. To address this, we used zinc, a low-pressure analogue of the hexagonal close pack (hcp) structured iron that forms the inner-core, to provide first-order constraints on the anelasticity of hcp-metals at high pressure, seismic frequencies (∼0.003-0.1Hz), homologous temperatures (T/T_m) up to ∼0.8. Measurements were made in a deformation-DIA combined with X-radiography. The data was analysed using an improved image processing method that reduces systematic errors and improves strain measurement precision by up to 3 orders of magnitude. Using this algorithm significant dissipation and softening of zinc’s Young’s modulus is observed. The softening occurs in the absence of significant impurities or a fluid phase and is caused by grain boundary sliding coupled with dynamic recrystallisation.The recrystallisation results in a steady-state grain-size and low dislocation density. A softened Young’s modulus predicts a reduction in shear wave speed 2-3 times greater than that for compressional waves, which is consistent with anelasticity playing a significant role in the seismic velocity of the inner-core. Comparison of elastic wave speeds from experimental or computed material properties with anelastically-retarded inner-core seismic velocities will tend to over-estimate the light element budget of the inner-core. Therefore anelastic effects in hcp-iron must be considered in the interpretation of the inner-core.