We establish a lower bound of \Omega{(\sqrt{n})} on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that \Omega(\sqrt{D(f)}) is a lower bound for all Boolean functions.Our technique extends a result of Ambainis, based on the idea that successful computation of a function requires ``decoherence'' of initially coherently superposed inputs in the query register, having different values of the function. The number of queries is bounded by comparing the required total amount of decoherence of a judiciously selected set of input-output pairs to an upper bound on the amount achievable in a single query step. We use an extension of this result to general weights on input pairs, and general superpositions of inputs.