Inhomogeneities in Ba2NaNb5O15 (BNN) single-crystal fibres undoped or doped with 1-5 at% Nd3+ and grown by the laser-heated pedestal growth technique were investigated by energy-dispersive X-ray microprobe analysis (EDXA), second-harmonic generation (SHG) measurements and interference contrast microscopy after chemical etching. The observed internal morphology of BNN fibres was correlated to SHG and EDXA measurements and involves convective flow instabilities in the molten zone and possibly unsteady interface kinetics. From this study, it appears that for a doping concentration equal to 3 at% Nd3+,no growth striations nor any kind of inhomogeneity could be detected, indicating, as also shown by differential thermal analysis, that this mixture congruently melts, ensuring very-high-optical-quality crystals are obtained as no cracks nor microtwins are also present for this amount of neodymium.