Single crystals of the three-dimensional frustrated magnet and spin liquid candidate compound PbCuTe$_2$O$_6$, were grown using both the Travelling Solvent Floating Zone (TSFZ) and the Top-Seeded Solution Growth (TSSG) techniques. The growth conditions were optimized by investigating the thermal properties. The quality of the crystals was checked by polarized optical microscopy, X-ray Laue and X-ray powder diffraction, and compared to the polycrystalline samples. Excellent quality crystals were obtained by the TSSG method. Magnetic measurements of these crystals revealed a small anisotropy for different crystallographic directions in comparison with the previously reported data. The heat capacity of both single crystal and powder samples reveal a transition anomaly around 1~K. Curiously the position and magnitude of the transition are strongly dependent on the crystallite size and it is almost entirely absent for the smallest crystallites. A structural transition is suggested which accompanies the reported ferroelectric transition, and a scenario whereby it becomes energetically unfavourable in small crystallites is proposed.
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