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SNARE proteins zipper to form SNAREpins that power vesicle fusion with target membranes in a variety of biological processes. A single SNAREpin takes about 1 second to fuse two bilayers, yet a handful can ensure release of neurotransmitters from synaptic vesicles much faster, in a 10th of a millisecond. We propose that, similar to the case of muscle myosins, the ultrafast fusion results from cooperative action of many SNAREpins. The coupling originates from mechanical interactions induced by confining scaffolds. Each SNAREpin is known to have enough energy to overcome the fusion barrier of 25-35 kB T, however, the fusion barrier only becomes relevant when the SNAREpins are nearly completely zippered and from this state each SNAREpin can deliver only a small fraction of this energy as mechanical work. Therefore they have to act cooperatively and we show that at least 3 of them are needed to ensure fusion in less than a millisecond. However, to reach the pre-fusion state collectively, starting from the experimentally observed half-zippered metastable state, the SNAREpins have to mechanically synchronize which takes exponentially longer time as the number of SNAREpins increases. Incorporating this somewhat counter-intuitive idea in a simple coarse grained model results in the novel prediction that there should be an optimum number of SNAREpins for sub-ms fusion: 3-6 over a wide range of parameters. Interestingly, in situ cryo-electron microscope tomography has very recently shown that exactly six SNAREpins participate in the fusion of each synaptic vesicle. This number is in the range predicted by our theory.