This paper describes high Q, free-standing, narrow beam supported film bulk acoustic-wave resonators (FBARs) fabricated with silicon micromachining. The resonators are composed of metal/ZnO/metal/Si(x)Ny (or metal/ZnO/metal) composite layers, which are suspended by narrow Si(x)Ny/metal (or metal) beams to minimize energy leakage to the substrate. A layer of 0.5-microm thick parylene deposited and patterned over the Si(x)Ny/metal (or metal) beams is proven to enhance the sturdiness of the free-standing structure greatly. The highest Q (quality) factors we have obtained with this new structure are 1,587 and 769 at 2.7 and 5.1 GHz, respectively. This paper also describes the effect of removing the silicon-nitride support layer (to form air-backed FBARs that do not use any supporting layer below or above piezoelectric the ZnO layer sandwiched by two metal layers). The electromechanical coupling constant (Kt2) is improved from 3.2% to 6.8% when a 0.9-microm thick silicon-nitride support layer is removed.