Data on Zandi sheep were analysed to quantify maternal and paternal imprinting, X chromosome and litter effects' contribution to phenotypic variation in birth weight (BW), weaning weight (WW), growth rate (GR), Kleiber ratio (KR), efficiency of growth (EF) and relative growth rate (RGR). To this end, a two step approach was adopted. In the first step, each trait was analysed with a series of 16 animal models, which were identical for fixed and autosomal additive genetic effects but differed for combinations of maternal permanent environmental, maternal genetic, X chromosome and litter effects. For each trait, the best model was selected by the Akaike information criterion (AIC) and likelihood ratio tests (LRTs). In the second step, three additional models were fitted by adding maternal imprinting, paternal imprinting or both (models 17, 18 and 19) to the best model selected in the first step. Estimators of bias, dispersion and accuracy of breeding values estimated within 19 models with whole, and partial data were used to evaluate how well were the 19 models in estimating breeding values for the animals when their records were masked. For all traits studied, fitting the litter effect led to a better data fit. Also, it resulted in noticeable decreases in residual variance and other maternal variances. For growth traits, models containing the X-linked effects fitted the data substantially better than corresponding models without the X-linked effects. For BW, WW and GR, estimates of X-linked heritability (h2s) ranged between 0.09 (GR) and 0.14 (BW). Ignoring X-linked effects from the genetic evaluation model resulted in significant inflated autosomal additive genetic variance. For BW, WW, EF and RGR, models containing the imprinting effects provided a better fit of the data than otherwise identical models. Imprinting effects contributed significantly to the phenotypic variation of these traits in a range between 5% (RGR) and 8% (BW, WW). A sharp decline was observed in autosomal additive genetic variance following including imprinting effects in the model (27% to 40% depending on the trait). The least bias and dispersion, as well as greater accuracies for breeding values of focal animals, were for a model which included imprinting, X-linked and litter effects. It was concluded that imprinting, X-linked and litter effects need to be included in the genetic evaluation models for growth and efficiency-related traits of Zandi lambs.