After a homomorphic transformation has been used to transform speckle noise into additive signal-independent noise, classic techniques are used to evaluate the number of discernible gray levels and the information capacity of images degraded by fully developed speckle noise. The probability distributions that we developed earlier are used to evaluate the required probabilities of error. Expressions are derived for square and for circular apertures. The information capacity is found to have a maximum of about 0.2 bits per speckle. The spatial frequency resolution required to obtain a given signal-to-noise ratio by spatial integration is evaluated.