: Is the following "shortening" allowed in fiction? I know you can write stuff like this: Head on pillow, I glanced at the clock. My mind made up, I went over to the counter. How

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This is well within the bounds of individual style. While not everyone might choose to write in this way, it isn't incorrect and may suit your particular "writer's voice."

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Second one is good. First sounds weird. Third one is begging for another sentence:

And with that he put on the climbing shoes, the harness, and attached himself to the rope. At the cliff's edge he rechecked every knot one last time. Everything set, he threw the end of the rope down the cliff, and began his descent.

Maybe put in a mutter:

And with that he put on the climbing shoes, the harness, and attached himself to the rope. At the cliff's edge he rechecked every knot one last time. "All set," he muttered. He threw the end of the rope down the cliff, and began his descent.

But, straight answer to your question is "yes."

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The middle one is fine, and the third one is okay. The first feels a little dodgy because you're veering close to a dangling participle, where you have a phrase which doesn't have a clear subject.
In the first and third sentences, the context clarifies the subject, but I'd rewrite them so you don't get into the habit of sloppy antecedents:

My head still on the pillow, I glanced at the clock.
And with that he put on the climbing shoes, the harness, and attached himself to the rope. With everything now set, he threw the end of the rope down the cliff, and began his descent.

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