The GDR notoriously had a national anthem ("Auferstanden aus Ruinen") whose lyrics (specifically "Deutschland, einig Vaterland") eventually became politically embarrassing, so that only its tune could be played on official occasions.
http://en.wikipedia.org/wiki/Auferstanden_aus_Ruinen
There is a poem by Brecht which might have been intended as an alternate candidate for GDR national anthem. Though probably not, because Becher's was officially commissioned; nevertheless it at least shows what Brecht thought a national anthem should be. It was published as "Kinderhymne" but in the typescript the title was just "Hymne" (anthem). Like Becher's lyrics, Brecht's were set to music by Eisler, but also fit Haydn's music that was used for "Deutschland über Alles." Brecht's anthem is clearly intended as a counter to "Deutschland über Alles"--note the third stanza.
Anmut sparet nicht noch Mühe
Leidenschaft nicht noch Verstand
Daß ein gutes Deutschland blühe
Wie ein andres gutes Land.
Daß die Völker nicht erbleichen
Wie vor einer Räuberin
Sondern ihre Hände reichen
Uns wie andern Völkern hin.
Und nicht über und nicht unter
Allen Völkern wolln wir sein
Von der See bis zu den Alpen
Von der Oder bis zum Rhein.
Und weil wir dies Land verbessern
Lieben und beschirmen wir's
Und das liebste mag's uns scheinen
So wie andern Völkern ihrs
The translation in Brecht's *Poems 1913-1956* (edited by John Willett) is as follows:
Grace spare not and spare no labor
Passion nor intelligence
That a decent German nation
Flourish as do other lands.
That the people give up flinching
At the crimes which we evoke
And hold out their hand in friendship
As they do to other folk.
Neither over nor yet under
Other peoples will we be
From the Oder to the Rhineland
From the Alps to the North Sea.
And because we'll make it better
Let us guard and love our home
Love it as our dearest country
As the others love their own.
(Some people actually did suggests this as the new German national anthem at the time of reunification, but of course they did not prevail...)