Al, you're starting at the wrong end for my application. If I wanted three tooth differences at the low end, I could keep the 12-27 and its 21-24-27 cluster, which would be easy to do since I ride a 12-23 in the three seasons and the 12-27 just sits in a box.
But it's the low end I want to narrow. The 23-25-27 of the 16-27 was the base I was going to start from.
Ok, didn't understand that before. In fact I was not aware of the 23-25-27 cluster. It looks like you could combine a 15-25 with a 16-27 to make a 15-27 but the cost would be high and you may not see that combination as an improvement.
Al