Here's my tip for dealing with veggies that are perhaps just a tad more mature than you might like. If your greenie beanies have been on the vine a day or two too long and gotten meaty and stringy instead of crisp and lean, if your carrots have been in the fridge just a shade too long and have lost some of their sweetness, cut them on the bias.
Cutting the beans on the bias allows the starchy seeds to fall out, leaving just the sweeter pods behind. It also exposes more of the bean to the heat, which softens it quicker without losing color.
Carrots cut on the diagonal cook quickly, again retaining color, and somehow they taste a little fresher. Vegetables prepared like this cook in less than five minutes in just a few tablespoons of water, so you don't lose what vitamins are left by pouring them off in the cooking water. And, if you add just a tad of butter while they steam in a covered pan, you can use far less butter for the same rich flavor than if you wait to add it at table.
All in all, I'm biased in favor of diagonally sliced veggies.