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I followed the overwhelming sentiment of TLS to keep my C&F addendum brief, but a strong regional school has requested more information prior to completing my app.
My current submission reads similar to:

"On (date), I was cited, but not arrested, and charged with brandishing a weapon at my home. On (date 3 years later), I plead no contest to a lesser charge of possessing a concealed weapon without a permit and received unsupervised probation and a $300 fine."

According to adcomms preliminary screening, this answer is incomplete and they want more information about the incident. This is the only school that has requested this based upon my addendum. How should I respond?

Um...tell them what happened? You apparently have a history of repeated weapons charges. On the surface, that looks bad. They want to know whether you, in a moment of psychotic rage, pulled a knife on your girlfriend (that would be bad), or whether a miniature swiss army knife that you forgot you were carrying fell out of your pocket while turning cartwheels on the quad at school (no problem). Just give them some minimal detail, without sounding like you're trying to avoid blame for your actions.