Is a search for a "seizable" item in a house unlawful as a general search?

However, if that which is seizable and the place where it is to be sought are specified by order of court or magistrate, the fact that search for it ranged at large throughout a house into areas where personal privacy is most in need of protection is not enough to render the search unlawful as 'general' if it was reasonable to suppose that the object of the search could be found where it was sought. E.g., Warden v. Hayden, 387 U.S. 294, 299--300, 87 S.Ct. 1642, 18 L.Ed.2d 782 (1967). Nor is the search invalidated by the fact that in attempts to identify that which was specified as seizable many unseizable items were examined and rejected, including some that were highly private.