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In disordered media, an interference effect called coherent backscattering (CBS) arises from the reciprocity of multiple scattering. When illuminating a medium in a given direction and measuring the intensity of scattered waves, one may observe an amplification around the backward direction. The angular extent of this amplification effect relates to the medium transport properties, which makes it an attractive tool for the characterization of heterogeneous media. However, exploiting this angular extent is challenging in practice because it is often too small to be reliably measured. Fortunately, the amplification of the backscattered intensity is not the only property of the CBS effect. Indeed, we observe an additional phase coherence between waves backscattered in different directions. As such, if the experimental configuration enables the complete measurement of backscattered waves, i.e., amplitude and phase, this phase coherence can be leveraged to enhance the CBS effect by a factor of 2 in both width and amplitude. This enhancement is key for more reliable measurements of transport properties and paves the way to the characterization of disordered media in challenging environments like biological tissues in vivo. In this work, we demonstrate the enhanced CBS effect theoretically and observe it experimentally with ultrasound waves.