By Charley Keyes, CNN Senior National Security Producer

Washington (CNN) - Ten days after the military dumped its "don't ask, don't tell" policy on gays and lesbians, the Pentagon has issued new rules allowing military chaplains to perform same-sex marriages, but only if allowed by law and the chaplain's beliefs.

"A military chaplain may participate in or officiate any private ceremony, whether on or off a military installation, provided that the ceremony is not prohibited by applicable state and local law," a memo released Friday says.

"Further a chaplain is not required to participate in or officiate a private ceremony if doing so would be in variance with the tenets of his or her religion."

The new policy allowing gays and lesbians to serve openly in the military went into force September 20. In May, before the end of "don't ask, don't tell," the Navy was forced into an embarrassing about-face when if first OK'd and then changed its mind on marriages on military bases.

The new military rules on marriages must be in line with the Federal Defense of Marriage Act and local laws.

The latest two-paragraph memo, from Under Secretary of Defense Clifford Stanley, carefully stops short of fully embracing the idea of same-sex marriage, saying that "a military chaplain's participation in a private ceremony does not constitute an endorsement of the ceremony by DoD" (the Department of Defense).