Mayers and independently Lo and Chau have shown that unconditionally secure quantum bit commitment is impossible. In this paper we show that under the assumption that the sender is not able to perform generalized measurements involving more than n qubits coherently (n-coherent measurements) then quantum bit commitment is possible. A commitment scheme is δ-binding if for each execution there is an \(\tilde x \in \{ 0,{\mathbf{ }}1\}\) that cannot be unveiled with probability of success better than δ. Our bit commitment scheme requires the transmission of N qubits and is δ-binding, for any δ > 0, if the committer can only carry out n-coherent measurements for some n ∃ Ω(N). For some α > 0, the scheme is 2−aN -binding against n-coherent measurements for some n ∃ Ω(√N). The security against malicious receivers is unconditional.