Machete, please
It's leads like this that cause the public to go dead on our reporting.
Baghdad, Iraq -- In the first sign of progress toward resolving the tense situation in Fallujah, coalition officials Monday issued a joint statement with civic leaders from the besieged city calling on armed insurgents there to turn in their heavy weaponry to avoid a new offensive by U.S. Marines.

Let me catch my breath. That's 46 words to fight through. The day of the week's in an awkward place; it uses "weaponry"; it repeats Fallujah three times (Fallujah, the besieged city, there), as if we didn't get it the first time, etc.

We can do better and actually get folks to read our stuff in the process, even the stories, like this one, that are about process.

Baghdad, Iraq -- Armed insurgents in Fallujah got a joint message from civic leaders and coalition officials Monday: turn in your heavy weapons or risk a new assault by U.S. Marines. It was the first sign of progress toward resolving the tense situation in that city.

Only three words fewer, but I think it reads about 20 words shorter.
If the two-sentence lede bothers you and you still like backing into your stories with prepositional phrases, try this:
Baghdad, Iraq -- In the first sign of progress toward resolving the tense situation in Fallujah, armed insurgents got a joint message from civic leaders and coalition officials Monday: turn in your heavy weapons or risk a new assault by U.S. Marines.

Only 39 words.