The family of rare-earth tritellurides RTe3 features charge-density-wave (CDW) order related to strongly momentum-dependent electron-phonon coupling. Similar to other CDW compounds, superconductivity is observed when the CDW order is suppressed via hydrostatic pressure [1]. What sets the heavier members of the RTe3 series apart is the observation of a second CDW transition at lower temperatures having an in-plane ordering wavevector , ∥ [ ] of almost the same magnitude but orthogonal to the ordering wavevector , ∥ [ ] observed at higher temperatures [2]. Here, we report an inelastic x-ray scattering investigation of the lattice dynamics of DyTe3. In particular, we show that there are several phonon modes along both in-plane directions, which respond to the onset of the CDW transition at , =. Surprisingly, these soft modes close to , = ( . , , ) show strong softening near , but do not exhibit any response to the lower-temperature transition at , = . Our results indicate that the low-temperature CDW order is not just the 90° rotated analogue of the one appearing at high temperatures.