Algebraic cancelling handles

Question

It is well known that handles of indices k and (k+1) may be cancelled if the attaching sphere of (k+1)-handle intersect the belt sphere of k-handle at exaclty one point. Is it also necessary condition for the cancelling? In Rourke and Sanderson book I found that for dimension $n\geq 6$ and for sufficiently small k the requirement of the uniqeness of the point of the intersection may be replaced by more weak condition that the belt and attached spheres have only intersection number equals to one. But since isotopic attaching maps give homeomorhic manifolds, it seems to very plausible that we can slightly move an attaching map to get more that one intersection points, but keep the manifold in any dimensions...