We prove a quantitative version of the following statement. Given
a Lipschitz function $f$ from the k-dimensional unit cube into a
general metric space, one can be decomposed $f$ into a finite
number of BiLipschitz functions $f|_{F_i}$ so that the k-Hausdorff
content of $f([0,1]^k\smallsetminus \cup F_i)$ is small. We thus
generalize a theorem of P. Jones [Lipschitz and bi-Lipschitz functions.
Rev. Mat. Iberoamericana 4 (1988), no. 1, 115-121] from the setting of
$\mathbb{R}^d$ to the setting of a general metric space. This
positively answers problem 11.13 in "Fractured Fractals and Broken Dreams"
by G. David and S. Semmes, or equivalently, question 9 from "Thirty-three yes
or no questions about mappings, measures, and metrics" by J. Heinonen
and S. Semmes. Our statements extend to the case of {\it coarse} Lipschitz
functions.