Five Christmas carols (5, 6, 5, 3 and 4 words respectively) have been re-arranged, and re-titled at 23/38 (4 words), 59/54/62D/5 (4 words), 87/12/74 (4 words), 20 (5 words) and 72/46A (3 words). A sixth carol (19 letters, 4 words) has been concealed in the grid under a new title (4 words), which must be highlighted. The initials of all six original carols can spell CUT BACK SWIM — COMFORT ICY DIGITS. Ignore an accent in 36D.
Across
1 Clocks measure time with seconds and musical rods (9)
8 Maths groups used for secret filming (10, two words)
15 Council reduced fare (4)
17 Get embarrassed once, when chap stripped me (6)
19 Poet is male but not good, having male characteristics (8)
21 Shocks the distressed may choose?