Nanometer-sized metallic necks have the unique ability to sustain extreme uniaxial loads (about 20 times greater than the bulk material). We present an experimental and theoretical study of the electronic transport properties under such extreme conditions. Conductance measurements on gold and aluminum necks show a strikingly different behavior: While gold shows the expected conductance decrease with increasing elastic elongation of the neck, aluminum necks behave in the opposite way. We have performed first-principles electronic-structure calculations which reproduce this behavior, showing that it is an intrinsic property of the bulk band structure under high uniaxial strain. ; This work has been supported by the Dirección General de Investigación Científica y Tecnológica of Spain (DGICYT) under Grants No. MAT95-1542, No. PB95-0202, and No. PB95-0061.