When one organization first shifted to agile, the team had trouble with maintaining the product backlog. No one could agree on priorities for items, they didn't know which item should be groomed next, and the backlog wasn't transparent to everyone. This team found a better method that works for them.
Prakash Pujar writes about his team's experience adopting some of the best agile practices to make their process extra lean and increase efficiency by increasing throughput—all without any change to the agile framework his team was following before and after. Here, he talks about some of the lean practices that worked for them.
I always recommend to teams newly transitioning to agile that they keep every iteration the same length. This helps them learn to manage their time, and after a few iterations they'll start to get a rhythm. Hopefully, they'll learn to work incrementally, doing testing and coding concurrently as part of one development effort, so that user stories are finished throughout the iteration, and testing isn't pushed to the last day.