A handwear (gloves or mittens) is provided for cleaning, washing, dishwashing, medical treatments, handy works, gardening, construction, etc., comprising: a flexible under-layer placeable over the hand, an over-layer placeable over the under-layer, and attachment means joining the layers. The over-layer comprises functional preferably disposable fragments situated in a finger, palm, or thumb sections thereof. In other embodiments flexible cover-shells are placed over the under-layer. The over-layer or cover-shells are made of at least one: steelwool, sponges, double pads, soap pads, rags, wiping materials, materials including medical ointments, creams, oils, glue, lubrications, special pastes, and polish. The attachment means are provided in one of the forms: Velcro™ strips, mechanical fastening, magnetic fastening, gluing, stitching, adhesive bonding, chemical bonding, weaving, fusion, thermal welding, and ultrasound welding, plastic sealing band. Some embodiments' under-layers are furnished with pockets, the fragments are made insertable into and removable from the pockets. Some pockets enclose soap-filled bags.