We present two applications of Ball’s extension theorem. First we observe that Ball’s extension theorem, together with the recent solution of Ball’s Markov type 2 2 problem due to Naor, Peres, Schramm and Sheffield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Second, we prove that the distortion required to embed the integer lattice { 0 , 1 , … , m } n \{0,1,\ldots ,m\}^n , equipped with the ℓ p n \ell _p^n metric, in any 2 2 -uniformly convex Banach space is of order min { n 1 2 − 1 p , m 1 − 2 p } \min \left \{n^{\frac 12-\frac {1}{p}},m^{1-\frac {2}{p}}\right \} .