This paper proposes a protocol to support mobility in the Internet with a new encapsulation technique. IP-squared (IP2). A basic idea to support mobility is as follows; 1) to define two IP addresses for each mobile host that indicate the host itself and its geographical location (logical and geographical identifiers), 2) to maintain an association of the logical identifier with the geographical identifier and 3) to continue communications between hosts by converting their logical identifiers to the corresponding geographical identifiers dynamically wherever they migrate. The association is called mobility binding. A goal of IP2 is to propose a mobility support feature which can simultaneously realize efficient routing paths to mobile hosts and less control traffics to maintain the mobility bindings into the current Internet Protocol without any modifications to both the conventional protocols and nodes. IP2 forms the efficient routing paths by enabling intermediate nodes to process the encapsulated datagrams. The key technique for this feature is a new header detection algorithm based on CRC checksum calculation and an effective usage of a header structure. Percentage of efficient routing paths can be adaptively controlled, depending on dispositions of the nodes which can en -and de capsulate datagrams appropriately based on the detection algorithm and the mobility bindings. The mobility binding must be updated whenever a mobile host migrates to another network. IP2 adopts an updating scheme combining self refreshment and on demand updating modes with taking a mechanism to form the efficient routing paths into considerations. It is shown that IP2 can acheive both an efficient routing path formation and a low traffic for mobility binding maintenance through analytical evaluations.