Knowing that a tetrahedral void is larger than an octahedral void, one might expect denser NaCl and NiAs-type structures to prevail at high pressures. However, an interesting feature of the topology of qtz systems, i.e. very high density, is used in the present work to propose new hypothetical highpressure phases with tetrahedral topology for the well-known III-V phosphides, BP and AlP, based on crystal chemistry and DFT studies. Gallium and indium phosphides are not considered here due to their dynamic instability (see section 3.5 for details).