Geoscientific models and measurements generate false precision (scientifically meaningless data bits) that wastes storage space. False precision can mislead (by implying noise is signal) and be scientifically pointless, especially for measurements. By contrast, lossy compression can be both economical (save space) and heuristic (clarify data limitations) without compromising the scientific integrity of data. Data quantization can thus be appropriate regardless of whether space limitations are a concern. We introduce, implement, and characterize a new lossy compression scheme suitable for IEEE floating-point data. Our new Bit Grooming algorithm alternately shaves (to zero) and sets (to one) the least significant bits of consecutive values to preserve a desired precision. This is a symmetric, two-sided variant of an algorithm sometimes called Bit Shaving that quantizes values solely by zeroing bits. Our variation eliminates the artificial low bias produced by always zeroing bits, and makes Bit Grooming more suitable for arrays and multi-dimensional fields whose mean statistics are important. Bit Grooming relies on standard lossless compression to achieve the actual reduction in storage space, so we tested Bit Grooming by applying the DEFLATE compression algorithm to bit-groomed and full-precision climate data stored in netCDF3, netCDF4, HDF4, and HDF5 formats. Bit Grooming reduces the storage space required by initially uncompressed and compressed climate data by 25-80% and 5-65%, respectively, for single-precision values (the most common case for climate data) quantized to retain 1-5 decimal digits of precision. The potential reduction is greater for double-precision datasets. When used aggressively (i.e., preserving only 1-2 digits), Bit Grooming produces storage reductions comparable to other quantization techniques such as Linear Packing. Unlike Linear Packing, whose guaranteed precision rapidly degrades within the relatively narrow dynamic range of values that it can compress, Bit Grooming guarantees the specified precision throughout the full floating-point range. Data quantization by Bit Grooming is irreversible (i.e., lossy) yet transparent, meaning that no extra processing is required by data users/readers. Hence Bit Grooming can easily reduce data storage volume without sacrificing scientific precision or imposing extra burdens on users.