My Vision+ binds perfectly with my original controller, but does not detect the new controller and will not bind to it. (I notice that my original controller beeps twice when I turn it on, whereas the new one beeps three times. I do not know if this is related to the issue.)   Can anyone help with this?

OK first and silly question is do you have the right replacement transmitter for the V+ ie. the 5.8GHz version ?

Two beeps = FCC mode, single beep = CE mode,  it's just the transmit power and won't have an effect on the ability to bind.  
You are following the binding instructions outlined in the manual?
You have the original transmitter powered off when you try to bind with the new one?
You power cycled your phantom prior to binding the new transmitter?
And yes to the prev. question is it a 5.8GHz transmitter? ( assume it would be if you have a new one with the camera tilt wheel )

One of the first things I learnt on this forum, is never to "assume" anything....

You can buy either the 2.4g or the 5.8 g transmitter right here at the DJI store.  They make both.

https://store.dji.com/product/2-4g-radio-controller

https://store.dji.com/product/5-8g-radio-controller-npvt

johnwarr.live Posted at 2015-2-5 02:30
One of the first things I learnt on this forum, is never to "assume" anything....

Yeah I know that's why I repeated your question

swomilan.hotmai Posted at 2015-2-5 02:01
Two beeps = FCC mode, single beep = CE mode,  it's just the transmit power and won't have an effect  ...

Oops ... now that you ask, I read the product description more carefully: "Upgraded Radio Controller 2.4G for the Phantom 2".  I realize now that it's not what I should have ordered. Thanks very much for your guidance!

Gerry1124 Posted at 2015-2-5 02:35
You can buy either the 2.4g or the 5.8 g transmitter right here at the DJI store.  They make both.

...

Thank you. I ordered the wrong one, which is why it wouldn't bind.

Indeed, thanks Rob for having the balls to come back and tell us the problem.