WARNING: for advanced bird owners with a solid relationship with their parrot only. Not for beginners, you'll only ruin your relationship with your parrot.
I've found it useful to tame my parrot by running at her or swinging my hand in really quickly to grab her and then rewarding her for it.
Sometimes when I'd get fed up with her or just need to put her away in a rush, she'd start flying away from me and it would turn into a game of chasing her back and forth across the room from perch to perch. This is not good and drives the flee from predator reflex. So what I've been doing is counter conditioning the natural response through flooding, desensitization, and positive reinforcement. I start slower and more gradually where I know she won't flee and just reach in and grab her, then I work my way up where I am running across the room full speed at her and grab her suddenly. Then when she's no longer flying away from this, I reduce the rewards and only reward this exercise on occasion.
This may sound silly but there can arise times when my parrot trusting me could mean life or death. Whether its outside and I need to grab her to save her from an animal or person or inside when she is near some dangerous object. By desensitizing her to an exaggerated situation in training, I can be more certain that I will be able to get her when I need to in a real scenario.
The only down side to having such a desensitized pet is that it could put it in danger from other people or animals because it will have a disarmed flee response. This is great for me at home and in controlled settings but I know I won't be able to free fly her because she doesn't have an adequate sense of danger. For this reason it is almost impossible to mix a good house pet parrot and an outdoor freeflight one. You're almost forced to have one or the other: A skittish parrot that flees at the sight of danger or any questionable situation or one that is so tame you can do pretty much anything to it.