We investigate the acoustical properties of uncompressed and compressed open-celled aluminum metal foams fabricated using a directional solidification foaming process. We compressed the fabricated foams using a hydraulic press to different compression ratios and characterized the effect of compression on the cellular microstructure using microtomography and scanning electron microscopy. The static airflow resistances of the samples are measured and related to the observed microstructural changes. We measured the normal incidence acoustical properties using two- and four-microphone impedance tube methods and show that the compression substantially improves their sound absorption and transmission loss performance. We then stack individual disks with different compression ratios to create various stepwise relative density gradient configurations and show that stepwise gradients provide a significant improvement in properties as compared to the uncompressed sample. The effect of increasing and decreasing relative density gradients on the overall absorption and transmission loss behavior is characterized. Finally, we use an experimentally informed and validated transfer matrix method to predict the effect of various layer thicknesses and stacking sequences on the global acoustical properties. Our results show that open-celled metal foams with stepwise relative density gradients can be designed to provide tailored acoustic absorption performance while reducing the overall weight of the noise reduction package.