red eye and zoom lens

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The zoom has nothing to do with it, really. Red eye is caused by having the flash pointing straight at the subject and too close to the optical axis of the lens.

Wouldn't the subject and the optical axis be on nearly the same axis with an extended zoom though?

Anyway, good advice on the bracket.

It was a horribly lit room. Some can lighting above. I had the ISO cranked up as far as I could tolerate it (1600), but it still was insufficient.