Stupid Headphone question

[Bass-desires]

Good morning yall,

I was wonding if the problem I'm having with my 'quiet practice' set-up is amp related or headphone related. I have a Ibanez 200 (passive pickups), little Peavy Max 126 amp to practice in my apt and don't want to piss of the others around me...so headphones. (not great ones) Koss all over the ear type about $20. My issue is when playing with the volume up, the lows get really badly distorted and fuzzy. And forget playing with a backround track with the volume up. Way too much distortion. This is headphone related, no?

What headphones can this poor bassist save up to get that will solve this problem?

Thanks guys,