Locally optimum vector quantizer (VQ) designs are presented for memoryless Gaussian, gamma, and Laplacian sources. For Gaussian sources, low (2-6) dimensional vector quantization provides relatively little improvement in mean-squared error (MSE) compared to the minimum mean-squared error (MMSE) scalar quantizer. For Laplacian or gamma sources, however, significant improvement in MSE is available with vector quantization. The Laplacian and gamma 6 bit, sixdimensional vector quantizers achieve, respectively, improvements of 2 and 4.5 dB over the corresponding scalar MMSE quantizer distortions.