In this chapter, we will discuss a procedure that uses a connection with the standard map to approximately determine the location of the first invariant spanning curve above the chaotic sea. The idea is to use the transition from local to global chaos exhibited by the standard map and describe the location of the invariant spanning curve for a family of two-dimensional discrete maps that admits the property in which one dynamical variable diverges in the limit where the other tends to zero continuously. Knowing the position of the first invariant spanning curve can be very useful for the scaling investigations to be discussed in the next chapter.