If the dielectric constant and dielectric strength be denoted by k and x respectively, then a material suitable for use as a dielectric in a capacitor must have 

The dielectric strength is the maximum electric field that a pure material can withstand under ideal conditions without breaking down. 

For high voltage capacitors we use practically high dielectric strength. If a material with a high dielectric constant is placed in an electric field, the magnitude of that field will be measurably reduced within the volume of the dielectric. 

This fact is commonly used to increase the capacitance of a particular capacitor design. 
So for good capacitors we require high K and high X.