keep (something) under one's hat, to

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.

Preserve the secrecy of something, as in I'll tell you about it if you promise to keep it under your hat. This usage alludes to hiding a secret in one's head, covered by a hat. [Late 1800s]

To preserve secrecy. This term, with its vivid image of hiding a secret under headgear, dates from the late nineteenth century and has remained current even though hats are worn much less frequently today. A popular song of the 1920s had it: “Keep it under your hat! You must agree to do that. Promise not to breathe a word” (quoted by Eric Partridge). See also in the dark.