One analysis is to say that e.g. [myself sick] is a **small clause**-- in effect a clause without the full range of verbal inflections, and that this small clause is in turn the complement of the main verb. Similarly:

> We consider [[David Cameron] [an excellent prime minister]].

the two NPs [David Cameron] [an excellent prime minister] would together be said to constitute a small clause, as would other cases such existential sentences in some languages (e.g. Russian) which can lack an overt verb.

Notice evidence from passivisation for not saying that the second complement is a "normal" object:

> David Cameron is considered an excellent prime minister by all UK voters.

> *An excellent prime minister is considered David Cameron by all UK voters.