Resource tradeoffs can often be established by solving an appropriate robust optimization problem for a variety of scenarios involving constraints on optimization variables and uncertainties. Using an approach based on sequential convex programming, we demonstrate that a substantial fidelity robustness is obtainable against uncertainties, while simultaneously using limited resources of control amplitude and bandwidth. What is required is a specific knowledge of the range and character of the uncertainties, a process referred to in the control theory literature as "uncertainty modeling". Using a general one-qubit model for illustrative simulations of a controlled qubit, we generate robust controls for a universal gate set. Our results demonstrate that, even for this simple model, there exist a rich variety of control design possibilities.