The seal and pressure against the earcups is crucial. I remember Dave Rat on YouTube doing an experiment with some Sennheiser HD-280 Pro headphones and noticed that the frequency response below 200Hz was attenuating badly. He applied a rigid object to the outside of the earcup and the attenuation went away and the full waveform appeared. This is an indication of poor damping in his setup and when the headphones are worn the issue usually goes away, but depending upon fit and the shape of ones head the issue may still be there.
Another great headphone that suffers from inadequate use and sealing is the Beyerdynamic DT1350. So many people have complained about these awesome headphones. I had similar issues until I properly adjusted the headband which increased the seal significantly. All of a sudden the headphones were amazing. The bass response went very deep while keeping the mid range quite flat. They even extend nicely into the treble.
I would say the seal is critical on a closed headphone and not quite as important on open headphones. Air movement is what sound is so if the seal it not right the sound waves will not be correct.
Some headphones due to comfort and seal can be bent gently to better fit around your ears. The V-Moda M80/V80 and Beyer DT1350 are perfect examples. They are made from a material that can flex and be formed much like most Grado headphones which is nice compared to their plastic counterparts like the ATH-M50.
Perhaps someone will chime in with a suggestion on how to get a better fit with your HFI-580 headphones.
