Carpentry tool one wants badly (5,3)

I believe the answer is:

tenon saw

I'm a little stuck... Click here to teach me more about this clue!

'carpentry tool' is the definition.
'tenon saw' can be an answer for 'tool' (I've seen this before). I'm unsure of the 'carpentry' bit.

'one wants badly' is the wordplay.
'badly' indicates anagramming the letters (letters in the wrong order).
'one'+'wants'='onewants'
'onewants' is an anagram of 'TENON-SAW'.

Can you help me to learn more?

(Other definitions for tenon saw that I've seen before include "Woodcutter" , "Tool - one wasn't (anag)" , "Carpenter's tool" , "One cuts" , "used in joint production" .)

I've seen this clue in The Telegraph.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.