Processes at their best are self-imposed sets of constraints that are empirically found to lead to better software (for whatever axes of 'better' makes sense for your team - faster, feature richer, higher quality, etc.) Scrum gives you a baseline set of rules to abide by. Any team who've worked with Scrum for more than a few months will start to tweak, add to or remove from these rules. If they're any good, they'll measure their tweaking and see what works and what doesn't. This is the whole point of having a retrospective.
As another example, if you want to include quantifiable performance bounds in your stories, do so. We work Scrum-ish, and we have a set of QA steps for every story implicit in its delivery (works across supported browsers, feels fast, immune to common security errors, etc). We test for this, and we demo it, but it's not articulated in every story. It's implicit in our work.