Audio-lossless robust watermarking (ALRW) is a new research issue in the field of information hiding, which can resist those content-preserving manipulations while can restore the cover audio files completely in case of no attacks. Most ALRW countermeasures proposed in the literature usually focus on additive noise-like manipulations such as MP3 compression, low-pass filtering and Gaussian additive noise, but few are resistant to challenging desynchronization attacks such as random cropping and time-scale modification (TSM). The main reason is that the exploited robust features in the existing ALRW algorithms are related to the sample position. In this paper, we propose an ALRW method by efficiently embedding a watermark into the histogram shape of the low-frequency component after the discrete wavelet transform (DWT) and reversibly hiding the distortion due to the robust watermark embedding as the compensation information for restoration of the cover audio file. The use of the histogram shape in the DWT low-frequency component as the exploited robust feature is: 1) mathematically invariant to TSM; 2) robust to random cropping attacks since an audio clip before and after the cropping often has similar distribution, and 3) resistant to interpolation errors during time scaling and those common audio processing operations. To reduce the compensation information, the robust watermarking process is elaborately and luminously designed to represent the difference between the original and the robust watermarked audio. As a result, an ALRW system against desynchronization attacks is achieved with satisfactory performance. Experimental results show that the proposed ALRW scheme can effectively reduce the compensation information and provide strong robustness to those common manipulations including TSM, random cropping, MP3 lossy compression and other noise-like manipulations. In case of no attacks, the cover audio signal can be recovered without any loss.