  We introduce three related but distinct improvements to multilevel Monte
Carlo (MLMC) methods for the solution of systems of stochastic differential
equations (SDEs). Firstly, we show that when the payoff function is twice
continuously differentiable, the computational cost of the scheme can be
dramatically reduced using a technique we call `Ito linearization'. Secondly,
by again using Ito's lemma, we introduce an alternative to the antithetic
method of Giles et. al [M.B. Giles, L. Szpruch. arXiv preprint arXiv:1202.6283,
2012] that uses an approximate version of the Milstein discretization requiring
no Levy area simulation to obtain the theoretically optimal cost-to-error
scaling. Thirdly, we generalize the antithetic method of Giles to arbitrary
refinement factors. We present numerical results and compare the relative
strengths of various MLMC-type methods, including each of those presented here.
