I usually throw my couplers and tips in a bowl of hot soapy water for a period of a few minutes, then scrub with a little cleaner that I purchased at Micheal's. It's made to use on couplers. This gets the threaded part of the coupler clean. Then I wash again with warm soapy water and rinse. Occasionally I boil them or clean them with vinegar.
so I can't just throw them into me.... ewww that would be one tough dinner
I put mine through the dishwasher as well. I put them in the little basket that I got to wash my daughters bottle nipples and sippy cup lids. It sits on the top shelf and keeps all my tips and couplers from falling to the bottom of the dishwasher.
I, personally, am also THE dishwasher in our home! I put a little dish soap in a cup or something, dip my tip brush or a small bottle cleaner brush in it, scrub the coupler, rinse in hot water. I haven't had any problems with greasy residue after washing like this. I also wsh my tips the same way. If I have any doubt that there is grease on them and I need them for royal icing, I will rinse in white vinegar, then hot water.
Tina
I have boiled mine in soapy water BRIEFLY then rinsed in vinegar to degrease. I have recently discovered the new Dawn Direct Foam. This stuff works really well. My featherweight bags that I have used over and over with buttercream come clean with no grease feel at all.
Now I maintain a separate set of tips, spatulas, couplers and bags for use with royal icing only, if this is why you are asking about this.
I either read it on here or heard it from my instructor last week (I make the bird this week too 
) that if you soak the tips and couplers in hot soapy water WITH vinager in it, they come out grease free. I tried it today when I decorated my cupcakes. The buttercream came off both the tips and the couplers with VERY little need for the brush ect, and were squeaky clean. I just used a good squirt of regular dawn, about 1/4 cup of vinager and hot hot water. I swished them around every few minutes but after about half an hour, only one coupler and two tips needed any sort of real cleaning. The rest just got rinsed. Hope this helps. 
I'm the dishwasher too and yes I've boiled my couplers with my tips before using them for royal icing work. I've not had a problem yet. I have also added like a drop or 2 of dawn to the water and kept and eye on it so the suds don't boil over. I give it a stir every once in a while and boil away for 2 minutes. Strain and rinse with more hot water then cool water.
Where I used to work we would put the dirty tips into a cup filed with club soda and then wash with soapy water after they had soaked awhile.
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