The Speaker drew comparisons with the springy Magic Roundabout character after concerns were raised by Patricia Gibson.
SNP MP Ms Gibson (North Ayrshire and Arran), raising a point of order, said she had had a “smear” perpetrated against her when a “snapshot of frozen film footage” was printed in a newspaper and it was suggested she was “asleep during proceedings” in the chamber.
She said video of the proceedings “demonstrated categorically I was not asleep”, adding that she had for a second or two “thrown my head back appealing to the heavens in despair at chuntering in the chamber” while one of her colleagues spoke.
Ms Gibson said she had faced an “outpouring of personal abuse” following the publication of the article.
The Speaker, in his reply, said it was an “extremely serious matter” for all MPs, before adding: “To be fair, she has just robustly refuted the allegation.
“The concern she has would be serious at any time, but it is a particular concern in what I think she described as the current febrile political atmosphere.
“She has put her view on the matter very clearly on the record and ... if she considers the allegations made against her might conceivably constitute a contempt of the House, she should write to me setting out the facts and I will adjudicate upon that.”
Mr Bercow also advised Ms Gibson to seek a debate on the matter before saying: “I have got a good vantage point in the chair ... I have never in my time in the chair observing (Ms Gibson) seen her fall asleep.
“She is a veritable parliamentary Zebedee, she is constantly jumping up and down - and that, as she knows, is a compliment not an insult.
“She is one of the most alert members of Parliament, one of the most assiduous chamber attendees and participants. She is without blemish so far as her parliamentary commitment is concerned.”
Mr Bercow then recalled how he once “momentarily” closed his eyes during a tennis match in “sheer suspense” but it was later suggested he might have fallen asleep - something he said was “inherently absurd”.