In experimental design the main aim is to minimise post-experimental uncertainty on model parameters by maximising relevant information collected in a dataset. Using an entropy based method constructed on a Bayesian framework it is possible to design experiments for highly nonlinear problems. However, the method is computationally infeasible for large design space dimensions. We introduce an iteratively-constructive method that reduces the computational demand by introducing one new datum at a time. The method reduces the multidimensional design space to a single-dimensional space at each iteration by fixing the experimental setup of the previous iteration. Both a synthetic experiment using a highly nonlinear parameter-data relationship, and a simplified seismic amplitude versus offset (AVO) experiment are used to illustrate that the results produced by the iteratively constructive method closely match the results of the global design method whilst only requiring a fraction of the computational time. This work thus extends the class of iterative design methods to nonlinear problems, extending fully nonlinear design methods to be applicable to real-world, higher dimensional geoscientific problems.