How to put wooden handles back on tampers

I have two tampers with broken handles. They are size 8"x8". I have reemed out the wood from the metal tamper head. I have cleanly cut the broken portion off the handles and have fresh(but shorter)handles ready to re-install. How do ya do it, please and thanks?
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They sell replacement handles for various tools, at home depot. If you re-use the shorter handles, use a hatchet to carefully chop and taper the tool end of the stick so it is slightly oversize, then just take a sledge and, with the tamper on cement, drive the handle home, so it is flush with the base of the tamper head. Then take some wedges or good sized nails to hammer into the head, to expand it against the tool. They sell axe, hammer, and sledge wedges at hardware stores. They work better than nails.
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