This study presents a new approach to obtain dominance estimates without using the full Henderson?s mixed model equations (MMEs) related to an additive plus dominance animal model. This reduction could decrease substantially the computing time and hence its cost. In contrast to a procedure that we proposed before, the method developed in this paper does not require D?1 and provides best linear unbiased prediction (BLUP) of genetic values that is close to that given by processing the full MMEs. In the previous study, we also elaborated an algorithm (denoted ?-REML) in order to approximate restricted maximum likelihood estimation of variance components via the expectation maximization (EM) algorithm. The ?-REML algorithm has been modified to be adapted to our new resolution approach. Through a numerical example, we show that there is a good agreement between REML-(EM), ?-REML and modified ?-REML estimates and that the latter algorithm is more efficient than our first proposition in terms of computing time and memory conservation.