I would construct a "smart fence" on both the northern and southern borders. Clearly delineate the border; fencing & nasty barbed wire would become superfluous. Webcams, infrared, motion & vibration (tunnel) detectors,  surveillance (radar,drone,  satellite) etc. Any intrusion could be promptly addressed. This should have been done long ago.

Illegal entry by defeating the authorized entry points is almost completely an all or nothing phenomenon i.e. if there are many areas of entry, illegal entry is thought of as not a big problem. Once the entire border has a smart fence, illegal entry becomes so difficult as to be not even worth the try.

9/19/2006 This is an update to this proposal. The smart fence would not be an actual fence except at access points. It would be a two lane blacktop with towers. The towers would have the equipment such as cameras, infrared, motion/vibration detectors, radar etc. with self-defense built in. Intermittent heliports at remote areas. There would be signs declaring the border and penalties for border violations. Any approach would be detected. Any violation could be promptly addressed by Border Patrol.