The design of compact spiral erbium-doped waveguide amplifiers (EDWAs) is considered under two constraints. The first one is the minimization of the chip area required for obtaining a predetermined gain, and the second one the maximization of the gain available from a limited area. It is shown that considerable benefit in gain and compactness of spiral EDWAs can be achieved by allowing tight bends with relatively high bend-induced losses. The effect of amplified spontaneous emission along with gain degradation on the noise figure in compact spiral EDWAs is analyzed. It is found that the dependence of the optimized limited area EDWA noise figure on the chip area attains a maximum at some definite area value. It is also found that there is a range of area values, where the optimized limited area EDWA noise figure is subjected to pronounced changes under small variations of the chip area. The study is based on a modified rate-propagation equation model that takes into account bend-induced losses in curved waveguides with varying radius of curvature. Numerical calculations based on actual waveguide parameters show the possibility of fabricating high gain, small size EDWAs.