Honestly, if you aren't doing this, you aren't doing "Agile", in the sense of the Agile Manifesto. If you are getting beat over the head by your scrum master with the "official Scrum process", you're not actually doing Agile. Scrum is an interesting toolbox to pull tools from; if you view it as a proscription, you're not doing Agile. Likewise for the other techniques offered by other people.
When people complain about fake Agile, I believe this is the big error that is being made.
I've done projects where we did 1 week iterations. I've done projects with story points and without. Right now I'm on a project where we're doing one iteration a month. And if you're about to jump up and try to explain to me why that's not "doing it right"... well, that's exactly what I mean. It turns out that for this project it's working great. We didn't start at that rate... we evolved into it when it became clear that 2 weeks wasn't useful for us.
See, my previous projects haven't had much use for the "sprint demo" but it's a critical part of this one, and we were noticing that neither the project team nor the customers were all that excited about the demos every 2 weeks, and we were running the risk of exhausting our customer's patience. This project isn't "customer facing" per se, and the tasks I get in this project aren't the sort where we need to do lots of UI explorations, where we need the demos very frequently to make sure we're going down the right track. Generally we get handend relatively well-defined tasks and our demos are more for convincing people progress is being made, getting feedback about priorities, and ensuring that the customers are happy and aware of what is going on. (The customers in this case are other developers in the organization.)
I offer that as an example of the sort of justification a team properly doing Agile ought to be able to provide for their choices. "Our Scrum book says" is not a reason to do something, or at least, it shouldn't be past the first 3 months.