I always find it a bit precarious lifting the battery out because you can only get your fingertips on just the top part really can't you. I make sure my hands are clean and grippy beforehand so there's less chance if it slipping and dropping back down. I also gently tie the terminals and securing strap just out of the way of the holder to give clear access in and out.
At least the Fazer battery is reasonably light. Those car batteries that don't come with a carrying handle are awkward to reach over and lower in sometimes. With all the plumbing and electrics that's under the bonnet nowadays 15kg of battery is the last thing you want to be dropping in there