The short answer: you can compress a video with no perceptible quality loss, but you cannot compress it with zero mathematical quality loss (unless the original is already poorly compressed). The distinction matters.
Three levels of "no quality loss"
Level 1: Mathematically lossless. Every pixel in every frame is bit-identical to the original. The output file, when decoded, produces the exact same image as the input. This is possible with lossless codecs (FFV1, HuffYUV, ProRes 4444 XQ). The problem: lossless video files are enormous. A 1-minute 1080p lossless video can be 5-10 GB. This is the opposite of compression for sharing purposes.
Level 2: Visually lossless. The output looks identical to the original when viewed at normal size on a normal screen. Pixel-level differences exist, but the human visual system cannot detect them. This is achievable with lossy codecs at high quality settings (H.264 at CRF 18, H.265 at CRF 20). File size reduction: 50-70% compared to the original.
Level 3: Perceptually acceptable. The output has visible differences from the original if you compare them side by side, but looks "good" on its own. This is the standard for most online video (H.264 at CRF 23-28). File size reduction: 70-90%.
Most tools that advertise "compress without quality loss" mean Level 2: visually lossless. This is a legitimate claim for single-generation compression at high quality settings.
When re-compression actually helps
If your original video was compressed with poor settings (very high bitrate for the content, no B-frames, outdated codec), re-compressing with better settings can produce a smaller file with no perceptible quality change. This is not magic; it is better compression of the same content.
Example: A screen recording tool that uses constant bitrate H.264 at 20 Mbps for a mostly-static screen. Re-compressing with VBR H.264 at CRF 23 produces a file that is 80% smaller with no visible quality change, because the original was using far more bits than needed for the content.
Example: A video encoded with MPEG-2 (used on DVDs) at 8 Mbps. Re-encoding with H.264 at CRF 23 produces a file that is 60-70% smaller at the same or better visual quality, because H.264 is a more efficient codec.
When re-compression causes visible loss
If your original video is already well-compressed (encoded with H.264 at CRF 23 or similar), re-compressing it at the same settings produces a file that is roughly the same size with slightly worse quality. This is generational loss. Each encode pass discards additional information.
Re-compressing at a lower quality setting (higher CRF, lower bitrate) produces a smaller file with visible quality reduction. This is the expected trade-off when file size is the priority.
The honest recommendation
For sharing and email: Compress at CRF 23-28. The file size reduction is significant, and the quality is excellent for all practical viewing scenarios. Do not worry about pixel-level differences that require A/B comparison to detect.
For archival: Keep the original file. Do not compress archival footage. Storage is cheap. Quality loss is permanent.
For professional delivery: Use visually lossless settings (CRF 18-20). The client gets a file that looks perfect, and it is smaller than the raw original. The MediaBrew compress tool applies these CRF targets directly in your browser without uploading footage to cloud servers.