While in Computer Science, grammar engineering has led to the development of various tools for checking grammar coherence, completion, under- and over-generation, in Natural Langage Processing, most approaches developed to improve a grammar have focused on detecting under-generation and to a much lesser extent, over-generation. We argue that generation can be exploited to address other issues that are relevant to grammar engineering such as in particular, detecting grammar incompleteness, identifying sources of overgeneration and analysing the linguistic coverage of the grammar. We present an algorithm that implements these functionalities and we report on experiments using this algorithm to analyse a Feature-Based Lexicalised Tree Adjoining Grammar consisting of roughly 1500 elementary trees.