Overshot and Swivel weaving (4shafts, 6 treadles).

    Overshot and Swivel weaving, give similar motifs as Welsh tapestry, but they're not doublewarp weaves, but doubleweft weaves. For most of them you'll only need 4 shafts and 6 treadles.
    The doubleweft consists of 1 pattern pick, followed by 1 tabby pick. Two bobbins, the pattern is often in a thicker yarn, while the tabby is woven in the same yarn as the warp or a thinner yarn. The tabby pick blocks the pattern pick and thus allows you to weave the same pattern pick, several times after another. The tabby picks rarely show in overshot drafts. 

    Overshot gives floats on both sides, but mirrored. As you can see on the photo, if there's a float at one side there's non on the other, and vice versa.
    Swivel is a form of overshot, the threading is the same. The treadling for the pattern picks is the threading rotated 90°. Each pattern pick is followed by a tabby pick, like for regular overshot. The tie-up is a straight 1,2,3,4 (shafts going down). The difference with overshot is, that there are no floats on the right side, they're all on the other side.

Whig Rose pattern in Overshot and Swivel.

Swivel Whig Rose threading, pattern treadling: 3255523

Inlaid swivel, woven by me for Handwoven, september 2012.

Sources: Donna Lee Sullivan, Weaving Overshot, Redesigning the tradition (Interweave Press, 1996).
www.handweaving.net , for drafts.