The relationship between strong and weak generative powers of formal systems is explored, in particular, from the point of view of squeezing more strong power out of a formal system without increasing its weak generative power. We examine a whole range of old and new results from this perspective. However, the main goal of this paper is to investigate the strong generative power of Lambek categorial grammars in the context of crossing dependencies, in view of the recent work of Tiede (1998)