Abstract: A joist support beam is comprised of an elongated substantially flat horizontal flange with a plurality of spaced upstanding brackets or web segments secured to the flange. Joist gripping elements are secured to the upper ends of the brackets and are comprised of hollow sleeves having threaded bolts therein which protrude in opposite directions therefrom. Plates are secured to the outer ends of the bolts for tight engagement with transverse joists extending across the plate in-between the upstanding brackets. A method of providing more headroom under joists using the aforementioned beam structure comprises positioning the beam structure so that the joists extend transversely across through the spaces between the upstanding web segments or brackets, extending the bolts from the sleeves for tight engagement with the joist extending across the beam. Alternatively, apertures are cut in the joists with a rigid member or sleeve placed within the aperture for the joist gripping means to tightly bear against.