An assembly can include a microelectronic element such as, for example, a semiconductor element having circuits and semiconductor devices fabricated therein, and a plurality of electrical connectors, e.g., solder balls attached to contacts of the microelectronic element. The connectors can be surrounded by first, inner regions 200 of compressible dielectric material and second, outer regions of dielectric material. In one embodiment, an underfill can contact a face of the microelectronic element between respective connectors or second regions. The second regions can provide restraining force, such that during volume expansion of the connectors, the first regions can compress against the restraining force of the second regions.