Near-micrometer resolution, three-dimensional computed tomographic images were made of a test object using the hard x-ray microscope developed by the National Institute of Standards and Technology (NIST). The microscope uses a cooled CCD camera with direct conversion of the incident x rays by a 512 multiplied by 512 chip with 19 micrometer by 19 micrometer cells. Magnification by a factor of 20 is achieved using asymmetric Bragg diffraction from a pair of silicon crystals. The imaging system is designed for samples of the order of 0.50 mm diameter by 0.50 mm height. From beamline X23A3 at the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory (BNL) 8.17 keV x rays were used. Two hundred, 512 multiplied by 512 two-dimensional projections were collected every 0.9 degrees about the test object using the NIST microscope. The projections were digitized and sent to a computer for volume tomographic reconstruction by a parallel-beam, convolution-backprojection algorithm into a 5123 image with (1 micrometer)3 voxels. The test object consisted of glass and nickel microspheres with distributions from about 4 t 40 micrometer (glass) or to 24 micrometer (nickel) diameters suspended in epoxy in order to demonstrate near one micrometer resolution in all three dimensions and probe contrast sensitivity. The effect and interplay of photon statistics and energy, and sample composition, density and size on tomographic performance are discussed as are resolution limitations and image artifacts from Fresnel diffraction.