1. A non-transitory computer-readable medium having stored contents that, when executed, cause one or more computing systems of an online service to: provide, by the online service and on a host computer system of the online service, a hosted virtual machine for use by a customer of the online service, including to store mapping information on the host computer system to associate a first virtual internet protocol (IP) address with the hosted virtual machine, and to use the stored mapping information for providing one or more communications to the hosted virtual machine; receive, by the online service and after the using of the first virtual IP address, a request to use a different virtual IP address with the hosted virtual machine on the host computer system; and initiate, by the online service and in response to the request, and while the host computer system continues to run the hosted virtual machine for the customer, a change for the hosted virtual machine from the first virtual IP address to a different second virtual IP address, including to update the stored mapping information on the host computer system to associate the second virtual IP address with the hosted virtual machine, and to use the updated stored mapping information for providing one or more additional communications to the hosted virtual machine.