Windows password change through different levels of RDP

There is conflicting and incomplete information on how to change your Windows password where RDP is involved. It turns out that the thing to do changes depending on how many levels of RDP are involved. Here's what I found:

• No levels of RDP. This is the simple case. Just Ctrl-Alt-Del then click on change password.
• One level of RDP. Just Ctrl-Alt-END (that's END, not Del) then click on change password.
• Two levels of RDP. You need to send Ctrl-Alt-Del to the machine at the end of the RDP chain but typing that will do it on the top level machine. Ctrl-Alt-END will do it to the machine at the second level of RDP. So you have to use the OSK command on the target machine to get an On Screen Keyboard. Then type Ctrl-Alt and click on the Del button on the OSK display.

If you google to find out how to solve this problem the most common reply is Ctrl-Alt-END. Here people are assuming there is only one level of RDP. It is very annoying that what you have to do depends on how many levels of RDP there are.