What kind of throw pillows will "stay put" on my new leather sofas?

Off the top of my head, they all slide off the smooth leather. But as an experiment, go to a department store and select the most likely to stay put on a leather couch, take them to the furniture section and see what happens on their leather couch. That's my best idea at this point. Good luck. Maybe another hometalker can help you better than this trial and error suggestion.

Soft squishy pillows that you can make the base a little wider than the top. Hard pillows that hold their shape are harder (pun intended) to mould.

You can sew or glue rubber shelf lining on the backs or in strips to grab the leather. You can also get paint on rug backing.

I draped a throw over the corner of my leather couch, to hide damage from cat claws, but the pillows stay on the throw.

Unfortunately that is a drawback of a leather sofa. That is why some people do not like them.

If make or buy pillows that are more "floppy-less filled" they tend to lay into the sofa and are very comfy and tend not to slide off as much as the tightly stuffed ones. The throw and coordinating pillow ideas is a good one that Brenda suggested. :)