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Christiana, I had a little trouble with those two as well; I think for 29d, the wordplay is to reverse and truncate a word meaning "shed" in the sense of "get rid of". I wouldn't ordinarily think of "shed" and the altered word as synonymous but the dictionary did confirm it.
For 44d, I felt the word "back" was misplaced for the clue to work correctly. Think of "secondly" in the sense of listing a group of items; what single letter might stand in here? Then "cut back supply" , reverse and truncate a word meaning "supply". (In fact if the word is "X", one definition of it is "to supply with X."). Except, the single letter goes on the end of this truncated word to make the abbreviation. Like I said I could not really get this one to scan properly, which might well mean I didn't understand it.