The present work employs the total-energy pseudopotential technique to calculate the relative stabilities at high pressures of the zinc-blende -Sn, and rocksalt structures in the series of compounds BN, BP, and BAs. For compressed volumes these compounds are shown to favor the rocksalt phase over -Sn, even though BP and BAs are the least ionic of the III-V zinc-blende compounds. This indicates that the stability of the rocksalt structure under pressure depends on more than just the ionicity factor. The structural preference is analyzed in terms of charge densities. The charge rearrangements at different volumes are also studied. We find that for BN the charge associated with B decreases with volume compression while the charge associated with N increases. In BP and BAs the opposite trend is observed, with P and As behaving like B in BN. BN appears to behave like a typical III-V compound semiconductor in its charge distribution while BP and BAs are anomalous cases which can be characterized by reversing the standard assignments for the anions and cations in these compounds.