*) just googled and apparently they way they "fix" it is to adjust one eye so it's good for long-distance vision, and the other so it's better for short-distance vision. So I suppose that might mean in my case I'd only need to have one eye operated on. Interesting idea...
They will recommend you get both done at once.
Reason for recommendation: it is the only way to give yourself a before/after objective comparison between the operated eye and an native unoperated eye. If you get both done at once you lose all perspective (groan). Also one at a time lowers your risks a little I think.
I got one eye done years ago, and have kept using a contact lens in the other (never operated on). I was not thrilled with the stellation, which you can only objectively judge if you have one unoperated eye. Using a contact lens is annoying, but the option of not using it gives me some extra superpowers.
My father in law just had his far sightedness corrected which is a more intense procedure (replace the lens). He had inflammation that lasted two months and he and his doctors weren’t happy with the results (seemed he had traded far sightedness for near sightedness) so they did laser and now he is shouting from the rooftops with happiness as to the result.