Properly apodized pupils can deliver point-spread functions (PSFs) free of Airy rings and are suitable for high dynamical range imaging of extrasolar terrestrial planets (ETPs). To reach this goal, classical pupil apodization (CPA) unfortunately requires most of the light gathered by the telescope to be absorbed, resulting in poor throughput and low angular resolution. Phase-induced amplitude apodization (PIAA) of the telescope pupil combines the advantages of classical pupil apodization (particularly low sensitivity to low-order aberrations) with full throughput, no loss of angular resolution and little chromaticity, which makes it, theoretically, an extremely attractive coronagraph for direct imaging of ETPs. The two most challenging aspects of this technique are (1) the difficulty of polishing the required optics shapes and (2) diffraction propagation effects, which, because of their chromaticity, can decrease the spectral bandwidth of the coronagraph. We show that a properly designed hybrid system combining classical apodization with the PIAA technique can solve both problems simultaneously. For such a system, the optics shapes can be well within today's optics manufacturing capabilities, and the 10-10 PSF contrast at ≈1.5λ/D required for efficient imaging of ETPs can be maintained over the whole visible spectrum. This updated design of the PIAA coronagraph maintains the high performance of the earlier design, since only a small part of the light is lost in the classical apodizer(s).