Genetic parameters for mean and for environmental variation in egg weight, body weight, age at first egg, and egg production were estimated in eight layer lines. The data were recorded from years 1999-2007, with on average of 6500 birds per line. An iterative mean-variance REML method was applied with a sire-plus-dam model for mean, a sire model for variance, and a fixed effect of hatch within generation for both mean and variance. The estimated heritability of environmental variation averaged about 5% for body weight, 3% for egg weight, and 11% for age at first egg, but was inconsistent among the lines for egg production (0-15%). Correlations between means and variances were slightly positive for body weight, egg weight, and age at first egg; and strongly negative for egg production. Age at first egg had the highest heritability of environmental variation; and favourable correlations with egg production and with variation in other production traits indicate that reducing variation in this trait may have potential benefits for the breeding industry.