In this paper, it is proposed to improve the quality of a variational description of a closed quantum system by adding fictitious dissipation that reduces the entanglement. The proposal is implemented for a small Bose-Hubbard chain in the mean field regime, which shows chaotic behavior and associated fast growth of quantum fluctuations. For appropriately chosen dissipation, good agreement with the truncated Wigner approximation is found. This shows that, when chaos leads to the breakdown of a variational method, adding fictitious dissipation can be a cure.