Connecting 1 1/4 inch drain tail piece to 1 1/2 inch waste line

I've replaced all the faucets and sinks in our house. The new standard for tailpieces (i.e. the drain pipe) appears to be a 1 ¼ inch diameter, but all the waste lines in my house are 1½ inches in diameter. They tell you you can use an adapter ring, but I found they didn't work so well. You can see the ring pushed up the pipe below:

 

It's not just the size difference that's a problem, as you can see above. It's also that the pipes just barely meet. That and the less than perfect hold of the adapter meant that the pipes weren't well connected; a good bump could separate them, which meant that under-sink storage would be a problem.

The solution was pretty simple. I got a 1½ extension. I pushed that over the 1¼ tail piece so they were doubled for a good 4 or 5 inches (I had to cut it to fit). I connected them with the same adapter and screwed on the compression ring as before. Then I connected the extension to the waste line. Since the differently-sized pipes overlapped for 4-5 inches, there was no chance of them separating, and having a 1½ to 1½ connection at the elbow meant that was a lot more secure than before. This is what it looked like after I put on the extension, but before I connected them:

 

Compare that to the first picture to get an idea of how much overlap there was. Below is what it looked like after, i.e., perfectly ordinary.