Like one part or another of minute without anxiety (10)

I haven't cracked this one yet — but the brilliant team at Times for the Times have:

Cryptic hint alluding to the two possible meanings of minute and the corresponding pronunciations.   My junior high football team was the Minutemen, and of course the 14-year-old wits used the pronunciation that made them Lilliputians instead of the heroes of Lexington and Concord.