This note explains an error in Proposition 5.1 of “Fibers of tropicalization”, Math. Z. 262 (2009), no. 2, 301–311, discovered by W. Buczynska and F. Sottile, and fills the resulting gap in the proof of the paper’s main theorem. Part (3) of Proposition 5.1 in [8] claims that if X is a subvariety of a torus T containing the identity then there is a split surjection φ : T → T ′ such that the image of X is a hypersurface and the intersection of the initial degeneration X0 with the kernel of φ0 is {1T }. This claim is false, and the following is a counterexample. Example 1 Suppose the characteristic of K is not 2, and let X be a curve in a threedimensional torus containing all eight 2-torsion points of T . Then X0 contains all eight 2-torsion points of T0 and, for any projection φ from T to a two dimensional torus, the kernel of φ0 contains four 2-torsion points, all of which are in X0. The falsehood of part (3) of Proposition 5.1 leaves an essential gap in the proof of Theorem 4.1, which is the main result of [8]. This result has now been proved independently by different means, including nonarchimedean analysis [4, Proposition 4.14] and noetherian approximation [7, Theorem 4.2.5]. The original proposed method of proof using split surjections of tori to decrease the codimension may be of independent interest, but the error in Proposition 5.1 interferes with the reduction to the hypersurface case. Here, we complete the proof of Theorem 4.1 via the original method of split surjections of tori by projecting even further, onto a torus of dimension equal to dim X , and using the going-down theorem for finite extensions of an integrally closed domain. The online version of the original article can be found under doi:10.1007/s00209-008-0374-x. S. Payne (B) Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven, CT 06511, USA e-mail: sam.payne@yale.edu