3D Gaussian Splatting (3DGS) has recently emerged as a promising contender to Neural Radiance Fields (NeRF) in 3D scene reconstruction and real-time novel view synthesis. 3DGS outperforms NeRF in training and inference speed but has substantially higher storage requirements. To remedy this downside, we propose POTR, a post-training 3DGS codec built on two novel techniques. First, POTR introduces a novel pruning approach that uses a modified 3DGS rasterizer to efficiently calculate every splat's individual removal effect simultaneously. This technique results in 2-4x fewer splats than other post-training pruning techniques and as a result also significantly accelerates inference with experiments demonstrating 1.5-2x faster inference than other compressed models. Second, we propose a novel method to recompute lighting coefficients, significantly reducing their entropy without using any form of training. Our fast and highly parallel approach especially increases AC lighting coefficient sparsity, with experiments demonstrating increases from 70% to 97%, with minimal loss in quality. Finally, we extend POTR with a simple fine-tuning scheme to further enhance pruning, inference, and rate-distortion performance. Experiments demonstrate that POTR, even without fine-tuning, consistently outperforms all other post-training compression techniques in both rate-distortion performance and inference speed.