Yes, that's just how the Triports are and the main reason why I sold them. A headphone amp might help to attenuate the overblown and bloaty bass and lack of treble, but the best solution is to use that money to get a better headphone to suit your needs. You can't fix a flawed headphone, get yourself a pair of Denon D1001K or Sennheiser HD 595, you'll be amazed how they blow the Triports away.
Thanks for your thoughts. I've since found the Accoustic setting in the ipod settings on the iPhone to give the best sound.
I'll probably stick with these ones for now and then try out the Denon/Sennheiser ones you've kindly suggested at a later date. I could do with finding a shop where you can try all the different ones out!
Try a 24hr+ burn in. Just plug them in and let them play. It will greatly enhance the sound.