Recently the effects of glass-host nonlinearities, particularly XPM and FWM, in EDFAs have received much attention . The reason is that in WDM communication systems these effects in typical EDFAs can be almost as large as in the transmission fibers themselves, and may affect communication system performance. Here we show theoretically that by using highly-doped waveguide amplifiers (EDWAs), which are just a few cm long, we can reduce these effects by several orders of magnitude compared to typical EDFAs which are several meters long. These effects remain moderate even if highly-nonlinear hosts such as tellurite or bismuth oxide are used; this may also open the way for the utilization of such materials, which are problematic for EDFAs. We have used analytical approximations as well as very accurate numerical simulations to calculate XPM and FWM in EDWAs and EDFAs. Nonlinearities are treated as a perturbation: we first calculate the power evolution for each wave along the amplifier, neglecting the effect of nonlinearities; we then use the power maps of all the relevant signals to calculate the nonlinear effects, by numerically integrating the corresponding differential equations. We will present the significant features of our simulation program, particularly the incorporation of the nonlinear effects. We will present examples of calculations for representative lengths, gains, and glass host materials, illustrating the considerable nonlinearity reduction achievable by using short waveguide amplifiers.