A ceramic thermal barrier coating (TBC) (18) having first and second layers (20, 22), the second layer (22) having a lower thermal conductivity than the first layer for a given density. The second layer may be formed of a material with anisotropic crystal lattice structure. Voids (24) in at least the first layer (20) make the first layer less dense than the second layer. Grooves (28) are formed in the TBC (18) for thermal strain relief. The grooves may align with fluid streamlines over the TBC. Multiple layers (84, 86,88) may have respective sets of grooves (90), Preferred failure planes parallel to the coating surface (30) may be formed at different depths (A1, A2, A3) in the thickness of the TBC to stimulate generation of a fresh surface when a portion of the coating fails by spalling. A dense top layer (92) may provide environmental and erosion resistance.