Cosmological textures are known from numerical experiments to isotropi
se as they collapse. This article studies general energy configuration
s having the same form of energy density as do textures. Straightforwa
rd arguments based on an extension of Derrick's theorem lead to the co
nclusion that textures isotropise because they lose energy in doing so
. The energy fraction lost in isotropisation is calculated. Since it i
s possible that some of the energy lost by macroscopic textures could
be radiated as gravitational waves, this fractional energy loss estima
tes the maximal energy fraction which could be produced as gravitation
al radiation during texture isotropisation.