In this paper the problem of off-line handwritten cursive text recognition is considered. A method for expanding the set of available training textlines by applying random perturbations is presented. The goal is to improve the recognition performance of an off-line handwritten textline recognizer by providing it with additional synthetic training data. Three important issues - quality, variability, and capacity - related to this method are discussed, and a basic strategy to make use of the possibility of expanding the training set by synthetic textlines is proposed. It is shown that significant improvement of the recognition performance is possible even when the original training set is large and the textlines are provided by many different writers.