We have been developing x-ray microcalorimeters for the Constellation-X mission. Devices based on superconducting transition-edge sensors (TES) have demonstrated the potential to meet the Constellation-X requirements for spectral resolution, speed, and array scale (> 1000 pixels) in a close-packed geometry. In our part of the GSFC/NIST collaboration on this technology development, we have been concentrating on the fabrication of arrays of pixels suitable for the Constellation-X reference configuration. We have fabricated 8x8 arrays with 0.25-mm pixels arranged with 92% fill factor. The pixels are based on Mo/Au TES and Bi/Cu or Au/Bi absorbers. We have achieved a resolution of 4.0 eV FWHM at 6 keV in such devices, which meets the Constellation-X resolution requirement at 6 keV. Studies of the thermal transport in our Bi/Cu absorbers have shown that, while there is room for improvement, for 0.25-mm pixels the standard absorber design is adequate to avoid unacceptable line-broadening from position dependence caused by thermal diffusion. In order to improve reproducibility and to push closer to the 2-eV goal at 6 keV, however, we are refining the design of the TES and the interface to the absorber. Recent efforts to introduce a barrier layer between the Bi and the Mo/Au to avoid variable interface chemistry and thus improve the reproducibility of device characteristics have thus far yielded unsatisfactory results. However, we have developed a new set of absorber designs with contacts to the TES engineered to allow contact only in regions that do not serve as the active thermometer. We have further constrained the design so that a low-resistance absorber will not electrically short the TES. It is with such a design that we have achieved 4.0 eV resolution at 6 keV.