We have no meanings for "nibbling a piece" in our records yet.
1 Ever and anon we alarmed the Turk by nibbling a piece nearer to his sacred city.
2 The seated man was nibbling a piece of venison on a broiling stick and did not look up.
3 He could not, however, refrain from nibbling a piece of biscuit, to try and stop the gnawings of hunger.
4 He was nibbling a piece of sugar as he drank his tea, and heaved a deep sigh at every sip.
5 Tony absent-mindedly nibbling a piece of roll already saw Dick in her mind's eye the victim of an assassin's blade.
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