Die (110) are attached to an interposer (420), and the interposer/die assembly is placed into a lid cavity (510). The lid (210) is attached to the top of the assembly, possibly to the encapsulant (474) at the top. The lid's legs (520) surround the cavity and extend down below the top surface of the interposer's substrate (420S), possibly to the level of the bottom surface of the substrate or lower. The legs (520) may or may not be attached to the interposer/die assembly. In fabrication, the interposer wafer (420SW) has trenches (478) which receive the lid's legs during the lid placement. The interposer wafer is later thinned to remove the interposer wafer portion below the legs and to dice the interposer wafer. The thinning process also exposes, on the bottom, conductive vias (450) passing through the interposer substrate. Other features are also provided.