An embodiment is a structure comprising a package, a substrate, and external electrical connectors mechanically and electrically coupling the package to the substrate. The package contains a die. The external electrical connectors are between the package and the substrate. An underfill material is around a periphery region of the package and between the periphery region and the substrate. A gap is between a central region of the package and the substrate, and does not contain the underfill material. The underfill material may seal the gap. The gap may be an air gap. In some embodiments, the underfill material may fill greater than or equal to 10 percent and no more than 70 percent of a volume between the package and the substrate.