Experience shows me (again and again) that agility is not about working fast but about finding elegantly simple solutions to business problems. You'll know you've found an elegantly simple solution when the business people agree it solves their most important and immediate problems and when the developers know the solution can be built and tested in 30 days or less.
Unless you find a solution that meets these two criteria, it's not possible to be agile. And often, because people can't find these simple solutions, they mistakenly claim that agility itself doesn't work. They come to this conclusion because they attempt to be agile by cramming complex solutions into short development cycles through working harder, longer, and faster.
That attempt has as much chance of success as trying to cram ten pounds of you-know-what into a five pound bag. Inevitably, the bag breaks, and then there is a mess to clean up.
An elegantly simple solution (a robust 80 per cent solution) doesn't do everything (there isn't time for that), just the most important things. Finding this solution is not easy; it's the creative part. It requires business people to figure out what tasks out of all the tasks they perform are the most important ones and what system features they need to handle those tasks. Then developers have to figure out how to build and test a system to deliver those features in the short amount of time available.
Business people need (at least temporarily) to suspend the notion that everything they do is complex and difficult (they can certainly revive that notion later when talking to the boss about a raise). A skilled JAD facilitator who walks them through a process mapping exercise will almost always be able to uncover those most important tasks because in drawing out the sequence of tasks in any workflow, and their inputs and outputs, it becomes obvious which tasks are the most important.
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