We are developing superconducting transition-edge sensor (TES) microcalorimeters for astronomical x-ray spectroscopy. We have obtained very high energy resolution (2.4 eV at 1.5 keV and 3.7 eV at 3.3 keV) in large, isolated TES pixels using Mo/Au proximity-effect bilayers on silicon-nitride membranes several mm wide. In order to be truly suitable for use behind an x-ray telescope, however, such devices need to be arrayed with a pixel size and focal-plane coverage matched to the telescope focal length and spatial resolution. For the Constellation-X mission, this requires fitting the TES, its thermal link, and contact wiring into a 0.25 mm square, a far more compact geometry than has previously been investigated. We have demonstrated that the weak thermal link can be restricted to a narrow (similar to10 micron) perimeter of membrane around the TES and still provide a thermal conductance in the acceptable range. Varying the size and placement of slits in that nitride perimeter, we can tune that value.