5-Point patches that cannot render -- a tutorial

In the animated GIF above, you see the creation of a spline mesh that was intended to be part of a TV remote control. It looks like a functional mesh, but the numerous (thirty-four!) dead-end splines create a situation in which nearly half of the 5-point patches the user wants to render cannot be selected as 5-point patches.

The mesh above was made in Animation:Master version 9.5, but everything in this tutorial applies equally to version 8.5.

What is a dead-end spline? Look at the image on the right. Ideally, every CP in a well-formed mesh should have two splines that pass through it. It's okay for a CP at the edge of a mesh to have only one spline passing through it and another that ends at the CP, but it is never a good idea to have more than two -- unless you really want massive creasing. Having more than two splines passing through a CP practically guarantees creasing. Especially if, as here, two splines pass through a CP and a third just butts up against it. That's a dead-end spline. There are two in the image on the right (colored green, with arrows pointing to them), and 34 in the mesh above.