We derive optimum values of parameters for laser-driven flights into low Earth orbit (LEO) using an Earth-based laser, as well as sensitivity to variations from the optima. These parameters are the ablation plasma exhaust velocity vE and specific ablation energy Q*, plus related quantities such as momentum coupling coefficient Cm and the pulsed or continuous laser intensity that must be delivered to the ablator to produce these values. Different optima are found depending upon whether it is desired to maximize mass m delivered to LEO, maximize the ratio m/M of orbit to ground mass, or minimize cost in energy per gram delivered. Although it is not within the scope of this report to provide an engineered flyer design, a notional, cone-shaped flyer is described to provide a substrate for the discussion and flight simulations. The flyer design emphasizes conceptually and physically separate functions of light collection at a distance from the laser source, light concentration on the ablator, and autonomous steering. Approximately ideal flight paths to LEO are illustrated beginning from an elevated platform. We believe LEO launch costs can be reduced 100-fold in this way. Sounding rocket cases, where the only goal is to momentarily reach a certain altitude starting from near sea level, are also discussed. Nonlinear optical constraints on laser propagation through the atmosphere to the flyer are briefly considered.