We say that a pair of points x, y is “secure” if there exists a finite set of blocking points such that any geodesic between x and y passes through one of the blocking points. The pair x, y is “midpoint secure” if all such geodesics have their midpoints in the blocking set. We will look at the relation between this two concepts, and how they relate to other geometric properties. The main point of this talk is to give the first example of a pair of points that is secure but not midpoint secure.