Implementing Scrum: step by step or by the book?

In my previous employment as a software development manager I decided, for reasons now irrelevant, not to implement Scrum "by the book". Instead, I implemented a continuous improvement process. Since the team believed in agile development and I am familiar with its concepts, things evolved in the right direction.

A year later I realized how close our process was to Scrum, making me wonder if we would have reached the same process faster by beginning with a "big M Methodology Implementation" of Scrum and letting the continuous improvement that is core to Scrum drive us from there.

When I joined Salir.com, I found myself managing a development team which completely lacked any process. We were essentially in "code and fix", management had a poor opinion of the team's productivity, and the team was burnt out by management's pressures and lack of appreciation.

So I thought there was little I could break and decided to implement Scrum "by the book". It took 1 sprint to hone things out, and on the second we were doing Scrum pretty right, according to this scrum checklist.

3 months later, the results are astonishing. The team has re-gained management's appreciation, and productivity is perceived as orders of magnitude higher.

I have concluded that, when the current process is unsatisfactory, implementing agile "by the Scrum book" is better than doing it gradually.

5-dec-2009 update: I've stumbled upon a posting where Rachel Davies advocates the gradual approach -- and where she discusses the criteria that should guide the decision for one approach or the other.