You can claim ownership via restricted channels, e.g. a phone call to key politicians, and rely on their self-interest to keep things quiet while understanding the threat.

In some cases, if the action is a bit too effective, you might even want to avoid it being pinned on you. Al Qaeda occasionally refused to claim ownership of things they very plainly did, and the Russians do it very often (e.g. when they shot down a Dutch passenger plane a few years ago).