Openfire 3.10 - Debian/Ubuntu and Java 7

On a Debian 7.7 server, the nightly Openfire 3.10 will not work with the compact “openjdk7-jre-headless” even when the install is forced. Others have also pointed out that the full non-headless “openjdk7-jre” installs a whole load of junk that is not desirable on a server. 3.9.3 for example, works fine with openjdk6-jre-headless.

Can 3.10 be made to work with the basic “headless” java package?