Because this part of a vehicle is in direct connection to the road and therefore subject to all of its imperfections, it is important that this weight be as low as possible, or at least much lower than the weight of the sprung part of the vehicle, in order that the wheels maintain optimal contact with the road surface. The greater the unsprung weight, the greater the inertia of the suspension, which will be unable to respond as quickly to rapid changes at the interface between the road and wheel. Unsprung weight can be reduced by using light alloy wheels, independent rear suspension (where the weight of the differential is not part of the unsprung weight), and front-wheel drive.
The classic design of rear-wheel drive through a live axle gives quite a high unsprung weight, which is one reason why it has fallen out of favour in the last 20 or so years.