A tubesheet for supporting closely spaced heat exchange tubes includes a plurality of sleeves or similar tubular members, through which the heat exchange tubes pass, disposed within a frame such that the longitudinal axes of all the tubular members are parallel. Preferably, each tubular member is welded or otherwise attached to the tubular member adjoining it. The frame is comprised of flanges that are normally welded or otherwise attached to the tubular members that adjoin them. The resultant tubesheet is stronger than conventional tubesheets having the same length of bridge wall separating the tube openings and therefore may be used to obtain a smaller than normal spacing between the tubes.