A method of making a screen for downhole use uses mesh screen layers that are diffusion bonded to each other. The ends that will overlap to make a seam when the sheets that are attached together are rolled into a tube are compressed before the tube shape is created or thereafter when the tube shape and an inner base pipe are drawn through a die to join the seam made by the overlapping edges. Because of the compression of the edges, when they overlap to form a tube the wall thickness at the overlap is about the same as the remaining thickness of the screen portion. Optionally, a resilient material can be compressed into the open areas of the screen portions that will be overlapped to make the generally longitudinally oriented seam. The seam can be parallel to the screen axis or spiral around it. The outer perforated shroud provides a compressive force that maintains a barrier resistant to flow of sand particles between the seam overlapping surfaces as the outer perforated shroud, filtration tube and inner base pipe assembly is drawn through a die.