This thesis was motivated by the collaborative research undertaken by QMUL and Pfizer UK into improving experiments at pre-clinical drug development. In theory, the most efficient designs for these particular experiments, as well as for many other studies, are optimal designs. Since, however, their implementation poses challenges — and several emerged during the project — optimal designs are uncommon in practice. To address these challenges the thesis introduces a comprehensive design framework, which both generalizes and simplifies optimal design. At the core of this framework are optimal relaxed designs, seldom considered before. Like a standard design measure a relaxed design has non-integer replications and is mathematically tractable; unlike the former, whose replications must sum to one, it allows the replications total to be unconstrained. The methodology discussed in this thesis assumes design of experiments for parameter estimation, given a response model, but also applies to broader problems. Although the motivation and applications come from the pharmaceutical project, the ultimate goal is to develop an intuitive and versatile design toolkit for experimenters in various practical fields.