The problem of optimal insulation thickenesses is one of the simplest that can be addressed by energy analysis. The authors begin witha simple analytical approach, and go on to describe detailed numerical work, based on the definition and parameterisation of a standard dwelling. Sensitivity of the results to large uncertainties in embodied energy data and building lifetime are investigated. The first conclusion is that insulation thicknesses in UK buildings are sub-optimal in energy terms. This conclusion appears to be robust. Energy-optimised dwellings in the climate of the UK would use more than 90% less energy for space heating than dwellings built to current standards. The authors also show that the penalty for non-optimal design is asymmetric, with much larger penalties for sub-optimal insulation thicknesses, than for super-optimal thicknesses of insulation. This suggests that under conditions of uncertainty, it is rational to install more than the central estimate of optimal insulation thickness.