A serious problem for covering law explanation is raised and its consequences for the Hempelian theory of explanation are discussed. The problem concerns an intensional feature of explanations, involving the manner in which theoretical law statements are related to the events explained. The basic problem arises because explanations are not of events but of events under descriptions ; moreover, in a sense, our linguistic descriptions outrun laws. One form of the problem, termed the problem of weak intensionality, is apparently solved by a simple logical move, but in fact the problem arises in a new, strong form. It is found that Hempel's model for deductive explanation (to which this discussion is confined) requires modification to handle the weak intensionality problem but then is faced with the problem of strong intensionality. In consequence, it is suggested that Hempel's important concept of explanation sketch is not as widely applicable as usually claimed, especially for explanations in the behavioral and social sciences and history. Reason is found to reject the covering law thesis that every scientific explanation must contain at least one law statement. An important feature of the discussion is that some of the main reasons given for altering the deductive model and for considering other forms of explanation are internal to the covering law theory.