I half the celery in the middle and peel a good amount of the skin (inside the U) away.
The carrots were the only fresh ones. They had bigger ones, but they were "old ones". Carrots, I peel, then half them lengthwise. Sometimes I cut them in half in the middle if they're too long. Then I make some horizontal slices, depending on the thickness 0-3. Then lengthwise thin slices ("vertical"), and then I chop. I don't know whether there's really something to do wrong, but maybe you've got an even better technique.