Error 1935 while installing Microsoft Office 2007, and I have .NET framework running fine

Office 2007 Enterprise fails to install on my fresh Windows 7 64-bit, with "Error 1935 ... HRESULT: 0x80070BC9". The advice online is to make sure .NET framework is installed, and it is - and running fine, for example paint.NET works.

Does it want some old .NET version perhaps?

I'm not sure what the problem was with .NET Framework, but I re-installed in Custom mode, and made sure to uncheck any components that had ".NET" in the name:

• .NET programmability for Excel
• .NET programmability for Word
• .NET programmability for PowerPoint

I think these are the only ones.