I have just begun using the tools recommended by seilogramp/Phil M and second his opinion of them. Your difficulty is not an uncommon one with a cheap snake. See his link above for the equipment. Also, great advice from him, I use a water-pic and flush my mouth before playing and it really helps keep the horn clean longer. (Ditto no eating and/or drinking sticky beverages on gigs.) Note also, his nice shortcut. If you clean the leadpipe every week the gunk won't get so far in the tubing; and if, you rinse your mpc after each use the plating will last longer, and if you also use a mpc brush on it once a week or so less gunk will get in the leadpipe. Have fun!