I make my coiled vessels with a coil and pinch method, usually starting out with a disk of clay to which I add coils one at a time, smearing the new soft coil into the drier, stiffer, most recent addition. I use a banding wheel in order to make the pinching, scraping and paddling consistent around the pot and achieve a more or less circular cross-section. It is a slow, rhythmic process that involves many individual movements of the thumbs and fingers to securely attach each coil and form the wall of the pot. I never spin the banding wheel to approximate a throwing type of pressure on the clay. The wheel revolves slowly as a result of the pinching or paddling. At the widest circumference of the piece in the photo there are around eighty thumb smears on the clay coil on the inside, as many on the outside, and as many pinches with both hands to thin and compress the coil and to extend it upwards and inwards or outwards, depending on the shape. When the coil is attached and thinned out, it adds two or three inches to the height of the wall. Then I use a serrated scraper to level the high places and work toward a more or less continuous surface (this usually involves another two or three times around the pot) and finally a paddle to further thin, extend, and shape the wall. The result is different from achieving a similar form by throwing on the wheel, where the clay is squeezed through the hands in a more or less horizontal direction with more speed and a more constant relationship to the central axis. Even though I am basically working toward a symmetrical and round form, the slow, hand methods result in a slightly out-of-round shape.
This process is perhaps less efficient than some of the traditional methods that use large coils and the palms or knuckles of the hands to smear the new coil into the existing wall, or using a paddle with an anvil on the inside to thin, compress and shape, but it is a method I developed while making some non-round, sculptural work several years ago. It allowed me to move the shape of the wall in any direction I wanted to as the form was being built and it also seemed to work well technically, in terms of having few problems with coil separation or other types of cracking.
As you can see in this image, four coils have been added so far. The challenge at the beginning, besides getting the shape you want, is to not add too much clay before the existing wall can support it. In a piece like this, I usually am able to add two coils to the bottom slab and pinch them up and outwards to the point where they are thin enough. The clay then has to dry enough to support more clay, so from then on, I am adding one coil at a time and letting it dry enough for the next one. In the above image I am gently paddling the last coil to get the shape I want.