keep under hat
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Related to keep under hat: keep under one's hat
keep something under one's hat
Fig. to keep something a secret; to keep something in one's mind (only). (If the secret stays under your hat, it stays in your mind. Note the use of but in the examples.) Keep this under your hat, but I'm getting married. I'm getting married, but keep it under your hat.
keep something under your hat
to keep something secret I've got some interesting news, but you must promise to keep it under your hat for the moment.