There are headphones from Bose, for whom I reserve a healthy contempt (whilst aware that they have their proponents so they must have /something/ going for them), which claim electronically to cut out background noise by the use of cancellation, in the form of inverting and amplifying the noise it picks up at the back of the headphone thus cancelling it out and preventing it from reaching your lughole. I've no idea if they are any good at that task. I have seen reports that say they are. But they are not purist enough for my taste. They (Bose) are a little bit Bang and Olufsen: design- rather than performance-led. Bit like a Mac, in fact. <Takes cover>.
If you are serious about possibly being in the market for a nupgrade then I think a world of ecstasy could await you. The difference between your 25 year old sibling-hacked 'phones and a pair of modern Sennheisers like Jon's or my lesser ones (his were >200 quid I think, mine were a "mere" 120 or so) will be absolutely stunning. At which point you might well decide to go for a better amp as well. Jon and I have (re-)discovered that even the differences between two supposedly top-end systems can be blindingly obvious, and more to the point one is usually easily identifiable as "better". Which means you tend to be loath to go back to the less good one.
If you would like to hear this amp/DAC combination once we've fired prototype II up without the use of a fire extinguisher, you'd be more than welcome. It is like lying on a lilo on a gently undulating azure sea with your eyes closed, whilst being drizzled from above in warm honey.
Although I suppose that might be slightly subjective.