Sometimes the thing that might have a codeword doesn't, as well. It's just refered to as a number (ie Op-Plan 4532334....yes, I made that up). Sometimes even the number will be classified, then the number/name gets declas but the actual plan is still class. Necessary, but still silly at times.
My personal favorite is the TACAID, which is CONFIDENTIAL/FOREIGN. Unfortuantely, whoever edits it doesn't pay attention to what they're labeling because things like brevity codewords (which are UNCLASS) and even the temperature conversion chart are labled as "CONFIDENTIAL."
You've hit on a pet peeve of mine - idiots who get excited about brevity words as though they're classified. On the other hand, we should all rue the day when the terrorists learn to convert Celsius to Fahrenheit.

