Phase I cancer trials are often thought of as have two competing aims: treating advanced stage patients at a dose close to the maximum tolerated dose (MTD) for their therapy, and active experimentation to obtain information about the dose-response relationship and an accurate estimate of the MTD for use in a subsequent phase II trial. Designs have been proposed to balance these aims, like "continual reassessment" by O'Quigley et al. (1990) and "escalation with overdose control" by Babb et al. (1998). As a benchmark for assessing these designs we consider an optimal sequential design, the computational complexity of which would limit its practical use for even a two parameter dose-response model, but which can be accurately approximated using recent computational advances in approximate dynamic programming and Monte Carlo simulation. We compare current designs to this near-optimum and discuss what intuition it can provide into the optimal balance between therapy and experimentation in phase I cancer trials. This is joint work with T.L. Lai at Stanford.