How to run a program in Windows as a limited user that requires administrator rights?

Question

Access rights

There is a program that requires admin rights to run. In the administrator user it works, but you need to make it run as a limited user.
If you set this checkbox in the program properties in the "Compatibility"->"Right Level"->"Run this program as an administrator" tab, then it works in Win7, but not in Win8 - UAC requires an administrator password.
There is an article www.oszone.net/10594 with some methods. But promising solution #4 only works for the admin, it doesn't work for the restricted one. Launching third-party programs is not suitable.