wires should be twisted together, cut shorter if it's too long then nutted. in school if my teacher sometime would take the wire nut to see if we twisted them or not then take points off if it wasn't twisted before nutted.
i remember someone telling when tightening the nut the rest of the wire should be twisted a few time. if the wire nut ever melts off(i've seen is happen) the wire wont just split a part and ground itself to anything.
other then for low voltage there's no reason to use anything but wire nuts.
i seen those lever connectors fail in ceiling lights. replace the connectors with wire nuts and it lighted right up.