Three blade-geometry optimization models derived along with assumptions from the blade element momentum (BEM) approach are studied by using a steady BEM code to improve a small horizontal-axis rotor of three blades that has been previously used in experiments. The base rotor blade has linear-radially varying chord length and pitch angle, while the other three models noted as Burton, Implicit and Hansen due to their references and characteristics yield blades of non-linearly varying chord length and pitch angle. The aim is to compare these rapid models and study how assumptions embedded in them affect performance and induction factors. It is found that the model that has the least assumptions (Hansen) and which considers the blade-profile drag in its optimization procedure yields the highest power coefficient, CP, at the optimal tip speed ratio (TSR), about 7% higher than the base one and also higher CP at high TSR. It produces an axial induction factor distribution along the blade that is closest to the 1D optimal value of 1/3. All optimized tangential induction-factor distributions along the blade closely vary as inverse to the square of the radial distance, while being mildly higher than the base distribution. It shows that sufficient swirl is necessary to increase power but at a level causing not too much energy loss in unnecessary swirl of the wake. At high TSR, all optimized rotors adversely produce higher thrust than the base one, but the one with most embedded assumptions (Burton) produces the highest thrust. Details of all three optimization models are given along with the distributions of the power, thrust, blade hydrodynamic efficiency and induction factors.