  We present {\it ab initio} and self-consistent tight-binding calculations on
the band structure of single wall semiconducting carbon nanotubes with high
degrees (up to 25 %) of boron substitution. Besides a lowering of the Fermi
energy into the valence band, a regular, periodic distribution of the p-dopants
leads to the formation of a dispersive ``acceptor''-like band in the band gap
of the undoped tube. This comes from the superposition of acceptor levels at
the boron atoms with the delocalized carbon $\pi$-orbitals. Irregular (random)
boron-doping leads to a high concentration of hybrids of acceptor and
unoccupied carbon states above the Fermi edge.
