We have achieved high-precision laser beam shaping by using a binary-amplitude spatial light modulator, a digital micromirror device (DMD), followed by an imaging telescope that contains a pinhole low-pass filter (LPF). An error diffusion algorithm was used to design the initial DMD pixel pattern based on the measured input beam profile. This pattern was iteratively refined by simulating the optically low-pass filtered DMD image and changing DMD pixels to lift valleys and suppress peaks. We noted the gap between the experimental result of 1.4% root-mean-square (RMS) error and the simulated result for the same DMD pattern of 0.3% RMS error. Therefore, we deemed it necessary to introduce iterative refinement based on actual measurements of the output image to further improve the uniformity of the beam. Using this method, we have demonstrated the ability to shape raw, non-spatially filtered laser beams (quasi-Gaussian beams) into beams with precisely controlled profiles that have an unprecedented level of RMS error with respect to the target profile. We have shown that our iterative refinement process is able to improve the light intensity uniformity to around 1% RMS error in a raw camera image for both 633 and 1064 nm laser beams. The use of a digital LPF on the camera image is justified in that it matches the performance of the pinhole filter in the experimental setup. The digital low-pass filtered results reveal that the actual optical beam profiles have RMS error down to 0.23%. Our approach has also demonstrated the ability to produce a range of target profiles as long as they have similar spatial-frequency content (i.e., a slowly varying beam profile). Circular and square cross-section flat-top beams and beams with a linear intensity variation within a circular and square cross section were produced with similarly low RMS errors. The measured errors were about twice the ultimate limit of 0.1% RMS error based on the number of binary DMD pixels that participate in the beam-formation process.