Constraining the reproduction alphabet to be of small size in encoding continuous-amplitude memoryless sources has been shown to give very small degradation from the ideal performance of the rate-distortion bound. The optimum fixed-size reproduction alphabet and its individual letter probabilities are required in order to encode the source with performance approaching that of theory. These can be found through a somewhat lengthy, but convergent, algorithm. Given reasonably chosen fixed sets of reproduction letters and/or their probabilities, we define new rate-distortion functions which are coding bounds under these alphabet constraints. We calculate these functions for the Gaussian and Laplacian sources and the squared-error distortion measure and find that performance near the rate-distortion bound is achievable using a reproduction alphabet consisting of a small number of optimum quantizer levels.