Erbium-doped Y2O3 integrated optical amplifiers are designed for low-threshold operation and 3 dB amplification. The most important design parameter for minimal threshold, the erbium concentration, is found to have an optimum value of 0.35 at% for a given waveguide structure with 1.0 dB cm-1 background loss. The corresponding threshold power is 7 mW. The pump power to obtain 3 dB gain is found to be 22 mW for an amplifier with an optimum erbium concentration of 0.6 at% and 2.8 cm length. At 30 mW pump power the maximum gain is shown to be 5 dB. Designing is done using a comprehensive numerical model of an erbium-doped integrated optical amplifier. In the model two-dimensional intensity-dependent overlap integrals are used, which allow arbitrary erbium dopant profiles and waveguide crosssections. Concentration-dependent effects such as quenching and upconversion are also included in the model. Input parameters for the model are determined from measurements on an unoptimized Er: Y2O3 optical waveguide amplifier. Amplification simulations and gain measurements of the unoptimized waveguides are found to be in close agreement, providing a sound basis for the design calculations.