We describe a new mechanism - what we call a booster draft - for allocating multiple, indivisible objects among a group of individuals. The mechanism's appeal lies in its strategy-proofness and simplicity: Individuals take turns drawing objects from different sets - called boosters - and simply need to identify their favorite object when it's their turn to choose. Following a market design approach, we examine how to tailor the booster draft mechanism to specific multi-object assignment problems. As an illustrative example, we consider the assignment of teaching positions to graduate students. We show that, through the right design of the boosters, not only is the mechanism strategy-proof, but the resulting allocations are fair and efficient. In fact, in the described domain, under some additional mild axioms, any strategy-proof mechanism is some variation of a booster draft. Finally, using data on graduate students preferences, we demonstrate that the booster draft is useful and easy to implement in practice.