In some cases all it requires is to put more curvature in the spring to get a stronger feel. It all depends on the size, weight, and travel of the key. Putting a thicker spring in a setting that doesn't require one can give the key the wrong "feel". I have run across this on vintage saxes that have had extensive work done over the years. In some cases the spring hole becomes enlarged and rather than address that specific problem, a thicker spring is installed in order to have a tight fit ignoring the ergonomics of the instrument.<update>
New needle spring installed. It wasn't quite as easy as I thought it was going to be (is blood always involved?) but thanks (again) to the Saxophone Manual it's now done and an improvement over how it was before.
To be honest, however, I think a perfect repair would involve reaming out the spring hole so that it would take the next size up of spring as it's still a smidge too light. I wasn't in the mood to try that, though.