In Italy, local public utilities are undergoing a radical change in organizational and market structure. The main aim is to extend contestability in order to introduce competition in those sectors. In fact, services are actually assigned to local public firms without auction (direct assignment); firms operate as legal territorial monopolists. Thus, Italian policy makers are planning to switch from a command-and-control kind of approach to a contract-based one, such as competitive tendering by auction (competition for the market). The adoption of the instrument of auction for local utilities, though, appears to be very difficult, mainly because of the multidimensionality of the output. The need to consider other variables than the price, such as quality, enforces to redefine the structure of the auction. The purpose of this study is to suggest a new, multilayered, form of auction, which would enable local policy makers to select local utilities firms considering both economic and qualitative variables.