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Disassemble the trombone by unscrewing the bell portion from the slide and removing the mouthpiece. Remove the outer slide and wipe off any excess grease, oil or moisture from the inner slides with a soft rag. Use a cleaning rod or a “snake” (a flexible rubber coated metal wire with a small brush on both ends), clean out any excess grease, oil or moisture from the insides of the outer and inner slides. Remove the main tuning slide from the bell portion and clean the inside with  a “snake”. Do the same for F attachment tuning slide if your trombone has the F attachment. If absolutely necessary, disassemble the rotary valve for the F attachment, rinse off each piece and wipe off excess oil or grease. Rinse all trombone components with warm water (NOT HOT, see warnings) in a shower or bath. Dry off all components with a soft rag, making sure that no large pockets of water remain in any of the tubing or in the rotary valve. Apply necessary grease to the tuning slides and attach them to the bell portion of the instrument. Reassemble the rotary valve and apply necessary oils. Apply necessary slide grease or oils to the inner slide. Wipe down the entire outside of the trombone using a soft rag.
Be careful not to bend or dent either slide in the process. Be gentle! If using a cleaning rod, be careful not to jam the rod into the bottom of the slide. If you are rough, you risk denting the crook at the end of the slide.   However, this stage of the cleaning should really be handled by a trained instrument technician, as any sort of scratch or dent in the valve will adversely affect the playability of the horn. Special attention should be given to the rotary valve, water key (or spit valve), and the outer and inner slides.   Most of the oil should be applied by dripping it in through the pipe where the bell section and playing slide meet, though a few drops may be applied to the rotary valve directly.