A device (22) for forming a tissue fold composed of two tissue layers is provided. The device (22) comprises a tissue chamber covered by a flexible-membrane sleeve (44). The device (22) is configured to form the tissue fold by drawing tissue into the tissue chamber in the device (22) through an opening in the flexible-membrane sleeve (44), upon the application of a vacuum to the chamber when the sleeve opening is placed against tissue. The sleeve opening has the form, as vacuum is applied to the chamber, of an elongate slit (48) having a gap dimensioned to restrict intake through the slit (48) of additional tissue layers, once the two tissue layers of the tissue fold have been drawn into the tissue chamber through the slit (48).
