While several analyses of polarimeter noise-reduction havebeen published, little data has been presented to support the analyticalresults, particularly for a laser polarimeter based on measurements taken atdiscrete, independent rotation angles of two birefringent waveplates. Thispaper derives and experimentally demonstrates the reduction of both systemand speckle noise in this type of laser polarimeter, achieved by optimizingthe rotation angles of the waveplates by minimizing the condition numbersof the appropriate matrix equation. Results are demonstrated experimen-tally in signal-to-noise ratio (SNR) variations for a range of materials andspatial bandwidths. Use of optimal waveplate angles is found to improvethe average SNR of the normalized Mueller matrix over speckle by a factorof up to 8 for a non-depolarizing material, but to provide little improvementfor a depolarizing material. In the limit of zero spatial bandwidth, theaverage SNR of the normalized Mueller matrix over speckle is found tobe greater than one for a non-depolarizing material and less than one for adepolarizing material.