A numerical model for erbium-doped waveguide amplifiers (EDWAs) containing bent waveguides was developed. The model uses rate-propagation equations and takes into account bend-induced losses in the waveguide with a varying radius of curvature. It is applied to the design of tightly packed erbium-doped waveguide amplifiers under two constraints: minimization of the area required to obtain a predetermined gain and maximization of the gain available from a given area. Numerical calculations based on realistic waveguide parameters demonstrate the possibility of fabricating high-gain, small-size EDWAs. Simple design rules, based on geometric formulas and consideration of bend losses, are given and compared with the results of numerical calculations.