A method of tissue compression is disclosed herein where the device to cause such compression is composed of a fastener bar and receiver. The device has the capability to self-adjust to tissues of varying thicknesses to cause hemostasis. This tissue gap variability allows for compression of regions of tissue where thick and thin tissue are both present. This variability also enables the same device to be used on a wide variety of tissues of different thicknesses. The tissue fastener bar of this invention contains a series of cut-out portions which distribute the compressive forces along the device in an alternating, staggered manner. The receiver is of a generally U-shaped configuration with the fastener bar being contained at least partially within the U-shape. Compression occurs between the side walls of the receiver and the fastener bar and variability in gap is accomplished by flexure of the side walls of the receiver. Varying side wall flexure is enhanced by cut-out portions in the receiver which allow each segment to flex somewhat independently. A number of options also exist for configuration of the fastener bar and/or receiver with the same basic method of compression being unchanged.