Coherent plane-wave compounding (CPWC) enables high-frame-rate ultrasound imaging, but the imaging quality is mainly determined by the beamforming method. Covariance-matrix-based statistical beamforming (CMSB) was previously proposed for synthetic aperture ultrasound imaging, which provides notable improvements in resolution and contrast over conventional delay-and-sum (DAS). However, the speckle quality is inadequate in the phantom experiment, and there exists a tradeoff between the contrast and speckle preservation of CMSB due to the constant diagonal reducing factor. In this paper, we applied CMSB in CPWC ultrasound imaging and propose an enhanced CMSB approach for CPWC to enhance the image quality. First, we introduced lag-one coherence (LOC) as an adaptive weighting factor for CMSB to suppress incoherent noise. Then, we propose adaptive diagonal reducing for CMSB using the coherence factor and amplitude standard deviation, with the aim to further improve the speckle quality. Finally, the combination of LOC weighting and adaptive diagonal reducing is proposed for CMSB to simultaneously improve the contrast and speckle quality. A simulation, experiments, and carotid studies were used to validate the imaging performance of the proposed methods. Results from the experiments show that LOC-weighted CMSB (LOCw-CMSB) with adaptive diagonal reducing improves the average contrast, generalized contrast-to-noise ratio (gCNR), and speckle signal-to-noise ratio (sSNR) by 59.9%, 53.6%, and 77.7%, respectively, in comparison with DMAS. The contrast and sSNR of the LOCw-CMSB with adaptive diagonal reducing were improved by 32.3% and 33.1%, respectively, compared to CMSB. In addition, LOCw-CMSB with adaptive diagonal reducing improves the contrast by 176.6% compared with SLSC in the in vivo carotid study, while it obtains a comparable gCNR. These results demonstrate that the proposed methods are effective in improving the image quality of CPWC imaging.