Light path gurus: Removing environment from reflections.

Hi all.

I am trying to render a building which is lit by an environment image in cycles.
But I do not want this particular image visible in the window reflections.

I have tried a lot with the light path node, but it just makes the window all black. Any ideas?

Well, if not that particular image, what else do you want to see reflected in the windows? Another image? Some uniform color?

In world cycles setup,
Two backgrounds mixed, Fac controled by Lightpath/is glossy ray.
So, light comes from a HDRI_a and reflections from a HDRI_b or anything else.