Well I just typed up a very long bit on my Jenday and what we do for screaming and my Macaw decided he was going to help me type and somehow deleted EVERYTHING! So I will now try and type up the short side of things before I get an assist from a bird. gah!
My Jenday screams for a few reasons that I have noticed. They are all VERY loud but I have noticed a slight difference between the screams.
Fun- He is just a happy bird and being very vocal. I let my birds have scream times. They love screaming when the radio is on, the vacuum is going....Loud times are happy times and the birds LOVE IT!
Calling me- if I leave a room and he screams I respond, "hello, how are you, what chu doing" if he screams more, i whisper the same things... normally that makes him lower his tone to a chatter.
scared- My Jenday is terrified of balloons. Well I have kids so there are balloons from time to time. He will freak out, scream, bite, and try to get away as fast as he can. So something very simple can cause a screaming fit.
attention screaming- this is where I do try and stop him. I ask him "where do the loud birds go? do you need a birdy time out?" That normally prompts him to stop because he has learned what is next. If he keeps on then I wait for a loud scream then I swoop him up real fast and take him to his cage in the bird room. Put him in and walk out closing the door behind me. I will wait till he stops screaming for at least a minute, then I will re enter. If he screams I will turn around and walk out, starting over. If I get him back out and he screams I will put him right back and start over. This process use to take a very long time before I got him all the way back out and on his central play stand. Now it almost never makes it to round two.
If I walk back in and he is quite from the start I will whisper to him. "what a good bird, lets go play" or whatever this is where he normally returns my whisper with a whisper chatter of his own and we make it his play stand without screams. Lots of rewards head scratches and even a treat for being quite once returning to his stand.
No joke... it use to take me a good hour of this. Now its over just as fast as it started.
Treat them like you would a two year old child. Normally a good solid week of standing your ground and it should get better, or it did with my Jenday.

) good luck