The purpose of this paper is to construct an operad ℋ_∞ with the good properties of both the little convex bodies partial operad and the little cubes operad used in May's theory of E∞ ring spaces or multiplicative infinite loop spaces ((6), chapter VII). In (6) ℋ can then be used instead of and , and the theory becomes much simpler; in particular all partial operads can be replaced by genuine ones. The method used here is a modification of that which May suggests on (6), page 170, but cannot carry out.