By Dan Williams

JERUSALEM (Reuters) - Military secrets are not readily divulged anywhere. But in Israel the blanket silence that envelops officials after an event like Wednesday's mysterious air strike on Syria reflects a deeper strategy involving both deterrence and outreach.

Beyond customary concern to safeguard spies and tactics for a government currently engaged in a graver confrontation with Iran, Israelis see such reticence as allowing their foes to save face and thus reduce the risk of reprisal and escalation.

Keeping silent, and so avoiding accusations of provocatively bragging of its exploits, also smoothes Israel's discreet cooperation with Muslim neighbors - such as Turkey or Jordan - who might otherwise feel bound to distance themselves.

Israeli leaders see benefit at home from not trumpeting successes that might give their public, or indeed Western allies, an exaggerated faith in their forces' capabilities.

And given international complaints that an unprovoked strike on a sovereign power breached international law, admitting the fact could only provide diplomatic complications.

So it was in 2007, when then prime minister Ehud Olmert muzzled his staff after the bombing of a suspected Syrian atomic reactor - a no-comment policy still in effect, though the United States has freely discussed that Israeli sortie and its target.

Olmert "wanted to avoid anything that might back Syria into a corner and force Assad to retaliate," the U.S. president at the time, George W. Bush, would recall in his memoir.

A former Olmert aide confirmed that account, telling Reuters the premier also feared for close military ties with Turkey, whose territory the Israeli warplanes crossed en route to Syria.

Israelis were then - as now - poised for a threatened war against arch-enemy Iran. Olmert, skeptical about whether Israel had the clout to take on the distant and much larger adversary, did not want to mislead his public by playing up the successful but far smaller-scale sortie against Syria next door.

"We knew the message of what had taken place would be received by the Syrian and Iranian leaderships, and that was enough for us," the ex-aide said on condition of anonymity.

So if Israel did attack a Syrian arms convoy headed to Lebanon's Hezbollah guerrillas, or a military complex near Damascus, around dawn on Wednesday, as described by various sources, a similar logic may now be keeping Prime Minister Benjamin Netanyahu, his cabinet and defense chiefs quiet.

Tackling the Iranian nuclear program is Israel's top priority, making it hesitant to lurch into other conflicts - especially with Syria's Assad government, an old enemy whose menace has faded, in Israeli eyes, with the two-year-old revolt.

Nor does Israel seek a flare-up with Hezbollah, which has mostly held fire since their 2006 war in southern Lebanon.

LINES AND ALLIES Continued...