Let S be a finite set of points in the plane that are in convex position. We present an algorithm that constructs a plane frac{3+4 pi}{3}-spanner of S whose vertex degree is at most 3. Let Lambda be the vertex set of a finite non-uniform rectangular lattice in the plane. We present an algorithm that constructs a plane 3 sqrt{2}-spanner for Lambda whose vertex degree is at most 3. For points that are in the plane and in general position, we show how to compute plane degree-3 spanners with a linear number of Steiner points.