Lossless compression can reduce climate data storage by 30-40%. In general, further reductions require lossy compression that also reduces precision. Fortunately, geoscientific models and measurements generate false precision (scientifically meaningless data bits) that can be eliminated without sacrificing scientifically meaningful data. 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 ACME data storage requirements by 40-80%. We compared Bit Grooming to competitors Linear Packing, Layer Packing, and GRIB2/JPEG2000. The other compression methods have the edge in terms of compression, but Bit Grooming is the most accurate and certainly the most usable and portable. Hence Bit Grooming provides flexible and well-balanced solutions to the trade-offs among compression, accuracy, and usability required by lossy compression. ACME and its user could reduce their long term storage costs, and show leadership in the elimination of false precision, by adopting Bit Grooming.