The increasing impact of electric vehicles on distribution networks can be alleviated by smart charging-the shifting of electric vehicle load to times when there is available capacity in the network. This work presents a market mechanism for smart charging that optimally allocates available charging capacity in a way that ensures network stability, while at the same time allowing vehicles to express individual preferences regarding their charging rates. Those who want higher rates can receive these, but must pay a higher price. The mechanism takes into account network-specific constraints such as total network load, voltage drop, and phase unbalance. However, since vehicles have differing impacts on these constraints, this leads to unequal access to the available resources (i.e., charging capacity), resulting in an unfair market. An additional constraint can be introduced to level the playing field for all users, but it leads to a reduction in aggregate performance. The mechanism is shown to be efficient and strategy-proof, so users cannot gain an unfair advantage by misrepresenting their preferences. A series of simulations demonstrate the mechanism's behavior and properties. The results open the door to multi-Tiered user plans by demand response aggregators.