Those Grado phones might be a good choice for that purpose.
The best I think are some on-ear, in-ear phones. Some of those run on nearly nothing. I have some Creative Aurvana's that aren't available anymore, and those babies biggest problem is sometimes you can't get them quiet enough without really dropping volume.
https://www.amazon.com/Creative-Ult...00U0WUI1O/ref=cm_cr_arp_d_product_top?ie=UTF8
These are similar to what I have, but not the same thing. They claim these are 110db/mw. I think the ones I have claim 114 db/mw. The ones I have sound pretty good, not great, a bit lightweight. But they are very comfortable, screen out lots of exterior noise, and being so easy to drive work great with a cell phone source.
There well may be better ones out there for around this price, but I think these types are going to be more efficient for low signal levels.