We use calculations based on density-functional theory in the virtual crystal approximation for the design of high-k dielectrics, which could offer an alternative to silicon dioxide in complementary metal-oxide semiconductor devices. We show that aluminates LaxY1-xAlO3 alloys derived by mixing aluminum oxide with lanthanum and yttrium oxides have unique physical attributes for a possible application as gate dielectrics when stabilized in the rhombohedral perovskite structure, and which are lost in the orthorhombic modification. Stability arguments locate this interesting composition range as 0.2<x<0.4. Phase separation in microdomains is shown to have the tendency to further enhance the dielectric constant. We propose this as a novel family of high-k dielectrics deserving experimental exploration.