We show that the colour-singlet contributions to the hadroproduction of J/ψJ/ψ in association with a W boson are sizable, if not dominant over the colour-octet contributions. They are of two kinds, sg→J/ψ+c+Wsg→J/ψ+c+W at View the MathML sourceαS3α and View the MathML sourceqq¯′→γ⋆/Z⋆W→J/ψW at order α3α3. These have not been considered in the literature until now. Our conclusion is that the hadroproduction of a J/ψJ/ψ in association with a W boson cannot be claimed as a clean probe of the colour-octet mechanism. The rate are small even at the LHC and it will be very delicate to disentangle the colour-octet contributions from the sizable colour-singlet ones and from the possibly large double-parton-scattering contributions. During this analysis, we have also noted that, for reactions such as the production of a J/ψJ/ψ by light quark-antiquark fusion, the colour-singlet contribution via an off-shell photon is of the order of the expectation from the colour-octet contribution via an off-shell gluon. This is relevant for inclusive production at low energies close to the threshold. Such an observation also likely extends to other processes naturally involving light-quark annihilation.