There's one point Melgas is right: ADK has to be preinstalled with only the box "Deployment Tools" checked, then add the WinPE tools. Installing the Deployment Tools afterwards works fine though. I have to apologize for this misinformation.
But resuming my point 1.: The ADK is not needed usually in Win 7 and higher. We use the WIM file of the "Windows Repair" environment. Only if this environment is not installed or corrupted the solution would be to use the ADK.
