Of interest is the analysis of results of a series of experiments repeated at several environments with the same set of plant varieties. Suppose that the experiments, multi-environment variety trials, are all conducted in resolvable incomplete block (IB) designs. Following the randomization approach adopted in Caliński and Kageyama (2000, Lecture Notes in Statistics, 150), two models for analyzing such trial data can be considered. One is derived under a complete additivity assumption, the other takes into account possible different responses of the varieties to variable environmental conditions. The analysis under the first, the standard model, does not provide answers to questions related to the performance of the individual varieties at different environments. These can be considered when using the more general second model. The purpose of this article is to devise interesting parameter estimation and hypothesis testing procedures under that more realistic model. Its application is illustrated by a thorough analysis of a set of data from a winter wheat series of trials.