This paper addresses a registration refinement problem and presents an accurate and fast Point-to-(Tangent) Plane technique. Point-to-Plane approach is known to be very accurate for registration refinement of partial 3D surfaces. However, the computation complexity for finding the intersection point on a destination surface from a source control point is hindering the algorithm from real-time applications. We introduce a novel Point-to-Plane registration technique by combining the high-speed advantage of Point-to-Projection technique. In order to find the intersection point fast and accurately, we forward-project the source point to the destination surface and reproject the projection point to the normal vector of the source point. We show that iterative projections of the projected destination point to the normal vector converge to the intersection point. By assuming the destination surface to be a monotonic function in a new 2D coordinate system, we show contraction mapping properties of our iterative projection technique. Experimental results for several objects are presented for both pairwise and multi-view registrations.