Pack the pipe properly, getting the tightness of the tobacco even, allowing for tobacco expansion if need be (refer to shag-cut tobaccos above).Some tobaccos need to be packed in a bit tighter to get the correct draw, try different packing techniques until you find the one that works best for your pipe/tobacco combination.
I have old pipes dating from the 1920's to the '60s from great English pipe making houses such as BBB, Comoy, DBL (Delacour Brothers) and of course Dunhill.
Way back in 1912, Dunhill created and patented the 'inner tube'.
The original purpose of the aluminum inner tube was to enable easier cleaning of the shank of the pipe.
Do your best to buy quality pipes, that is, pipes that are constructed properly with an unrestricted draw, open mouthpieces, and well cured briar.
Make sure the pipe is clean, inside as well as outside.
Remember, this was before commercially available pipe cleaners.