Objectives: The aim of this study was to evaluate Cu-64 PET phantom image quality using Bayesian Penalized Likelihood (BPL) and Ordered Subset Expectation Maximum with point-spread function modeling (OSEM-PSF) reconstruction algorithms. In the BPL, the regularization parameter β was varied to identify the optimum value for image quality. In the OSEM-PSF, the effect of acquisition time was evaluated to assess the feasibility of shortened scan duration. Methods: A NEMA IEC PET body phantom was filled with known activities of water soluble Cu-64. The phantom was imaged on a PET/CT scanner and was reconstructed using BPL and OSEM-PSF algorithms. For the BPL reconstruction, various β values (150, 250, 350, 450, and 550) were evaluated. For the OSEM-PSF algorithm, reconstructions were performed using list-mode data intervals ranging from 7.5 to 240 s. Image quality was assessed by evaluating the signal to noise ratio (SNR), contrast to noise ratio (CNR), and background variability (BV). Results: The SNR and CNR were higher in images reconstructed with BPL compared to OSEM-PSF. Both the SNR and CNR increased with increasing β, peaking at β = 550. The CNR for all β, sphere sizes and tumor-to-background ratios (TBRs) satisfied the Rose criterion for image detectability (CNR > 5). BPL reconstructed images with β = 550 demonstrated the highest improvement in image quality. For OSEM-PSF reconstructed images with list-mode data duration ≥ 120 s, the noise level and CNR were not significantly different from the baseline 240 s list-mode data duration. Conclusions: BPL reconstruction improved Cu-64 PET phantom image quality by increasing SNR and CNR relative to OSEM-PSF reconstruction. Additionally, this study demonstrated scan time can be reduced from 240 to 120 s when using OSEM-PSF reconstruction while maintaining similar image quality. This study provides baseline data that may guide future studies aimed to improve clinical Cu-64 imaging.