We report the results of a detailed inelastic neutron-scattering study of renormalization of the bondstretching phonons in optimally doped YBa 2 Cu 3 O 6+x ͑YBCO͒. In agreement with previous work, this renormalization is strongest halfway to the zone boundary in the ͓010͔ direction where it manifests itself as a transfer of phonon spectral weight from ϳ60 to ϳ50 meV. Phonon renormalization begins on cooling from well above the superconducting transition temperature, T c , but strongly accelerates at T c . In contrast with the La 2−x Sr x CuO 4 system, where a similar longitudinal phonon anomaly occurs, the anomaly in YBCO appears to extend in the transverse direction along the branch that connects the longitudinal mode at the in-plane wave vector q in = ͑0 , 0.25͒ and the transverse bond-stretching mode at q in = ͑0.25, 0.25͒. Therefore, phonon renormalization in YBa 2 Cu 3 O 6.95 seems to be consistent with a quasi-one-dimensional behavior.