While several analyses of polarimeter noise-reduction have been published, little data has been presented to support the analytical results, particularly for a laser polarimeter based on measurements taken at discrete, independent rotation angles of two birefringent waveplates. This paper derives and experimentally demonstrates the reduction of both system and speckle noise in this type of laser polarimeter, achieved by optimizing the rotation angles of the waveplates by minimizing the condition numbers of the appropriate matrix equation. Results are demonstrated experimentally in signal-to-noise ratio (SNR) variations for a range of materials and spatial bandwidths. Use of optimal waveplate angles is found to improve the average SNR of the normalized Mueller matrix over speckle by a factor of up to 8 for a non-depolarizing material, but to provide little improvement for a depolarizing material. In the limit of zero spatial bandwidth, the average SNR of the normalized Mueller matrix over speckle is found to be greater than one for a non-depolarizing material and less than one for a depolarizing material.