We prove that every metric space which admits an l_1-tree as a Lipschitz quotient, has a sigma-porous subset which contains every Lipschitz curve up to a set of 1-dimensional Hausdorff measure zero. Banach spaces containing l_1 represent a particular case of such metric spaces. As a corollary we obtain an infinite-dimensional counterexample to the Fubini theorem for the sigma-ideal of sigma-porous sets.