The idea that I have experimented with is a loose adaptation of Cann (1996). Cann (1996) argues that certain constructions can be doubly headed by two elements, so that the label of the phrase marker is a union of two separate heads. In the case of 'walk with a limp' the verb 'walk' might be the primary head. The secondary head, which in this case might be the adverbial 'with a limp' might then stand in the Specifier of V position, and its properties migth be determined by some higher governing head. In other words, I suggest that the verb 'walk' is the primary verbal head, whereas the adverbial 'with a limp' is the secondary head occupying the Specifier of V position. The label of the phrase marker is some kind of a union of the qualities and the semant ics of both the verb and the adverbial. The adverbial 'with a limp' occupying the Specifier of V position has, in Finnish, the second infinitive intrumental form of the verb 'limp' so the adverbial might then possibly be analysed further as some kind of a projection of the instrumental case, selecting an infinitival complement. So far I have not analysed these constructions in great detail, but, at least as a first approximation, they seem very promising in that they are able to explain why the distributi on of the Specifierless phrase is different from that containing a Specifier. Only the specifierless phrase, ie the phrase which receives the stage level reading, can combine with certain types of adverbials, such as adverbials of time and place. The phra se containing the Specifier, ie the phrase that receives the individual level reading, cannot combine with certain types of adverbials.