We investigate the optimal relationship between the aerodynamic power, thrust loading and size of a wind turbine rotor when its design is constrained by a static aerodynamic load. Based on 1-D axial momentum theory, the captured power P for a uniformly loaded rotor can be expressed in terms of the rotor radius R and the rotor thrust coefficient CT. Common types of static design-driving load constraints (DDLCs), e.g., limits on the permissible root-bending moment or tip deflection, may be generalized into a form that also depends on CT and R. The developed model is based on simple relations and makes explorations of overall parameters possible in the early stage of the rotor design process. Using these relationships to maximize P subject to a DDLC shows that operating the rotor at the Betz limit (maximum CP) does not lead to the highest power capture. Rather, it is possible to improve performance with a larger rotor radius and lower CT without violating the DDLC. As an example, a rotor design driven by a tip-deflection constraint may achieve 1.9% extra power capture P compared to the baseline (Betz limit) rotor. This method is extended to the optimization of rotors with respect to annual energy production (AEP), in which the thrust characteristics CT(V) need to be determined together with R. This results in a much higher relative potential for improvement since the constraint limit can be met over a larger range of wind speeds. For example, a relative gain in AEP of +5.7% is possible for a rotor design constrained by tip deflections, compared to a rotor designed for optimal CP. The optimal solution for AEP leads to a thrust curve with three distinct operational regimes and so-called thrust clipping.