Earcup headphones capable of producing low frequencies

I bought headphones that were supposed to produce down to 15 Hz like -3 dB but they were producing 20 Hz like -10 dB.
I know it's up to other components as well but I find them disappointing for headphones with such large membranes, not to mention they began to rattle at low frequencies.
I am not willing to spend a fortune, otherwise I would buy something really expensive and there would be no need of this thread.
I ask if somebody has come upon a decent piece for a reasonable price.