A short, small kind of panier, sometimes identified with the janséniste, sometimes with what in English is called pocket hoops: Two small "cages" of calico or linen with each three rows of boning in tunnels, slightly flaring, attached to a waistband. One sat over each hip, so they were also called "false hips". Both had a slit at the top into which a pocket, also attached to a waistband, could be hung. But as the pocket hoops were closed at the bottom, they could also be used as pockets in their own right - hence the name.
Piton describes considérations as small paniers used for morning wear, without further information on their shape. He could mean pocket hoops or something else entirely.