Oh that's true, my headphones with noise canceling were also over-the-ear. I found that turning on the noise canceling worked great and brought down the sound of a lawnmower really well by playing sound waves opposite the waves of the motor to cancel each other out. I wasn't thinking about another pair of ear buds.

The wireless headphones that I was using went around your head and didn't pump the sound directly into your ear, but were supposed to use some bone conduction. I'm not sure if that's part of the battery issue that I saw. I just know that my phone itself would die before the end of my shift if I was using Bluetooth headphones (provided the headphones didn't die first) and I would still have battery left after using wired earbuds.