"undecorate" is not a word. ... "If not, then how does one describe, in a single word, the process of removing decorations from a Christmas tree?"Most people I know of talk about "taking down" the tree but I agree with your bride, first you have to "undecorate" it.
When we decorate a cake, we never have to undecorate it because it is made to be eaten.
When we change the decorations in a room, we redecorate it. We are not rotating the decorations in and out of storage, as we do with Christmas decorations. We are bidding farewell to the old decorations forever.
When we decorate a Christmas tree, we can't throw the tree out with the tinsel. We have to undo the decorations.
Your bride is not only sweet, but serenely reasonable.
Too often we assume that all the words we will ever need have already been fashioned. We just have to go rummaging around for them. Your bride knows better.
She has just filled a gap in our vocabulary ... and you are a very lucky man to have both qualities in the same lady, Father Steve.
I hope you will honor her edict, and also her innovation.
Happy New Year.
