Google returns a lot of versions of 'My Pigeon House', almost all through oral transmission (the expression 'learned this from my grandmother' occurs with remarkable frequency!) The origin is less verifiable: some are claiming Russian, some Germany, some Austria. I asked my German and Austrian contacts if they were at all familiar with the song, and my German friend found this:

DAS TAUBENHAUS

Ich öffne jetzt mein Taubenhaus,
die Täubchen die fliegen so froh heraus,
sie fliegen hin aufs grüne Feld,
wo's ihnen gar zu wohl gefällt;
doch kehren sie heim zu guter Ruh',
so schließ' ich wieder mein Häuschen zu,
doch kehren sie heim zu guter Ruh',
so schließ' ich wieder mein Häuschen zu.

Though I don't speak German, this is obviously the same song ("I open the doors of my pigeon coop, they fly out, into a green field, I close the doors of my house...", or, amusingly as Babelfish renders it, "I open now my pigeon house, which Taeubchen fly so gladly out, it fly on the green field, wo's them too probably pleases; but they turn home too better rest ', then lock ' I again my little house, but turn her home too better rest ', then lock ' I again my little house."...)

However, what seems odd is that I can't make the lyrics fit the tune of either Pigeon House (as we sing it on this continent) or Muss Ich Den, with its short repeats.

Any German-speakers out there, or others who would also like to claim this for their old-country grandmother? :)

I and my mother have done a professional recording of this and hope to get it online at some point - AFAIK the only version available on line. Let me know if you 'catters have discovered others!