The cristobalitelike forms of the ternary silica analogues BPO4 and BAsO4 were investigated at high pressure by x-ray diffraction and theoretical methods. The behavior of these compounds represents an extreme case in which the tilt angle of the constituent tetrahedra increases in a spectacular way at high pressure resulting in a major change in topology from a cristobalitelike framework towards a "collapsed cristobalite" structure. These compounds provide the first examples of the collapse of a framework structure to a close-packed form in a continuous manner without an intervening phase transition.