The size of an LR(k) parser essentially depends on the number of different LR(k) tables or states of the parser which is always bounded by y \(2^{| G|^{k+1}}\). However, it appears to be rather difficult to prove that this or any other double exponential upper bound is strict. In this paper, the author shows that such a bound is too conservative for many important subclasses of context-free grammars. In particular, it is shown that for non-right recursive grammars the number of LR(k) states is at most \(| G|^{k| G|}\). \(2^{| G|}\). Some other classes such as the left linear and the right linear grammars are also analyzed. Examples of grammars with large LR(k) parsers are given.