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Dual apodization with cross-correlation (DAX) is a novel adaptive beamforming technique which utilizes two distinct apodization functions in suppressing side lobes and clutter. Previous studies have shown that the performance of DAX in minimizing the effects of phase aberration diminishes with increasing aberrator strength. To achieve greater improvement in image contrast, we propose, in this paper, to combine DAX with a phase aberration correction algorithm based on nearest-neighbor cross-correlation (NNCC). Our simulation and experimental results presented in this work showed that the proposed method allows for synergistic enhancements of image contrast and achieves greater improvement in image quality than using DAX alone or phase aberration correction alone in the presence of weak and strong aberrators. Compared with standard delay-and-sum (DAS) beamforming, using the proposed method on simulated data with weak and strong aberrations increased the contrast-to-noise ratio (CNR) values from 4.10 to 10.96 and from 1.69 to 9.80, respectively. Experimental results were obtained using pork tissues of 4 and 10 mm thickness and a tissue-mimicking phantom. The CNR values increased from 3.74 to 9.72 for the 4-mm pork aberrator and from 1.27 to 8.17 for the 10-mm pork aberrator.