Single crystals of (Bi1-xPbx)(2)Sr2Ca2CU3O10+delta (x = 0 and 0.16) (sizes up to 3 x 2 x 0.1 mm(3)) have been grown by means of a newly developed "vapour-assisted travelling solvent floating zone" technique (VA-TSFZ). Post-annealing under high pressure of O-2 (up to 10 MPa at T = 500 degrees C) was applied to enhance T-c (up to 111 K) and improve the homogeneity of the crystals (Delta T-c <= 1 K). The structure of both Pb-free and Pb-doped Bi-2223 was refined for the first time from single crystal X-ray diffraction (XRD) data. The unit cell of the average structure is pseudo-tetragonal with a = 5.4210(7), b = 5.4133(6) and c = 37.010(7) angstrom, and a = 5.395(l), b = 5.413(l) and c = 37.042(11) angstrom, for the Pb-free and the Pb-doped phase, respectively. An incommensurate modulation in the direction of one of the short cell vectors has been defined (q similar to 0.21 a*), however, the structure can be conveniently described in a supercell with a fivefold volume (a = 27.105(4) angstrom). With respect to the "non-modulated" structure, one additional oxygen atom for ten initial O was found to be inserted into the BiO layers. The superconducting anisotropy of Bi-2223 was found to be similar to 50, from measurements of the lower critical field. The anisotropy of Bi-2223 is significantly reduced compared to that of Bi-2212, and this accounts for the enhanced irreversibility fields in Bi-2223. Furthermore, Bi-2223 has a higher critical current density, and a reduced magnetic relaxation rate compared to Bi-2212, which are both signatures of more effective pinning in Bi-2223 due to its reduced anisotropy. (C) 2007 Elsevier B.V. All rights reserved.