We introduce Bit Grooming, a lossy compression algorithm that removes the bloat due to false precision, those bits and bytes beyond the meaningful precision of the data. Bit Grooming is statistically unbiased, applies to all floating-point numbers, and is easy to use. Bit Grooming reduces data storage requirements by 25–80 %. Unlike its best-known competitor Linear Packing, Bit Grooming imposes no software overhead on users, and guarantees its precision throughout the whole floating-point range.