This study explores progress achieved with 2DOF, 3DOF, and MDOF acoustic liners constructed with mesh caps embedded within a honeycomb core. These liner configurations offer potential for broadband noise reduction, and are suitable for conventional aircraft implementation. Samples for each configuration are tested in the NASA normal incidence tube and grazing flow impedance tube, with and without a wire mesh facesheet. Impedances based on these measured data compare favorably with those predicted using a transmission line impedance prediction model. Predicted impedances are then used as input for an aeroacoustic propagation code to compute axial acoustic pressure distributions in the grazing flow tube. These predicted distributions compare favorably with the corresponding measured distributions at frequencies away from the frequency of peak attenuation, but suffer slight degradation for frequencies very near the peak attenuation frequency, where the predicted results are sensitive to input impedance changes. As expected, the noise reduction frequency range increases as more degrees of freedom are included. Although the specific results achieved herein may differ from those that would be achieved with other 2DOF, 3DOF, and MDOF liners, this comparison highlights some of the key features that can be exploited in the design of parallel-element, embedded mesh-cap liners.