In my current translation project I have several sentences which end with a clause without a verb. I would like to do this in the corresponding German as a way to be concise and avoid putting too many descriptive words and phrases in front of a noun. For example:
This is a small piece of paper, fit for a carrier bird.
I could translate this word for word into German as:
Das ist ein kleines Stück Papier, für einen Trägervogel geeignet.
If I simply put everything in front of the noun it would look like this (I believe this is considered awkward):
Das ist ein kleines, für einen Trägervogel geeignetes Stück Papier.
But when I plug this sentence into Google Translate it adds a relative pronoun and verb to the clause like so:
Das ist ein kleines Stück Papier, das für einen Trägervogel geeignet ist.
It seems to me that the first translation above is more concise, but is this wrong grammatically, or considered bad style by native German speakers?