+1 to what captsouisie said. First 2-3 careful turns with a drill bit that barely fits, then gradually larger drill bits up to the manufactured size of the mortise.
Be very careful not to enlargen the mortise! A bad, non-flush fit of tenon into mortise will a) make the stem be loose and b) contribute to condensation and thus gurgle/wet smoke! Always drill by hand, NEVER drill with a powertool! Think of it as carefully reaming the mortise.
With a bunch of pipes, I have also opened up the draft hole to 4mm during this step of the cleaning process for a more open draw.
After 'reaming' you will still need to clean out the mess. A shank brush like this will save you a good amount of Bristle Pipe cleaners:
I usually take two bowls, one filled with hot water, the other filled with 99% Isopropyl Alcohol. Then I fill up the inside of the bowl with cotton balls, press them all the way down to real tight. They will absorb the excess alcohol that will unavoidably get through the draft hole into the bowl and weaken up the heel of the bowl.
First clean the brush in the hot water bowl, dry it with a kitchen paper towel, then dip it into the alcohol and scrub the mortise and draft hole. Rinse, Repeat. When water discolours, get fresh one. Until the shank brush comes out fine. If you have done no previous Alcohol bath treatment or the like, this process that can easily take up to two/three hours. As a final step, I then do the same procedure with Qtips instead of the shank brush. Until they come out clean. Takes between 10-50 Qtips usually depending on how good you worked with the shank brush ;-)
Don't give up. Cleaning gooed up shanks is probably my least favourite step of restoring estates. It always feels like those goddamn brush will never again come out clean. If you are persistent and keep scrubbing, eventually it will.
Good Luck!