|Try this old W95 program "WinSize" which keeps your settings fine:-|
It is OK on W98SE so there is a fair chance it will be OK on WinME. It caused a file handling issue with XP NTFS (Windows hiding behind each other) otherwise I would still be using it now.
If it doesn't start automatically put a shortcut to the exe file in Startup. When you close the "Window Handler" use the close program button rather than the corner X otherwise it will need restarting.
You can save screens any old size and position so long as they have not been saved maximised (ie pull them to size instead). Just tag then save the Window. There are also options to centralise, use wildcard Window names and so forth.
Hope it works for you on WinME because it's a great little program.
some other bloke...