Whether you need an amp largely depends on the firebox. I am not familiar enough with it to tell you whether or not you need a headphone amp, but if that firebox has enough power to drive the headphones (and I don't just mean power to sound loud, I mean power to sound refined and unstrained), then you don't need a headphone amp.

It's also a matter of whether the headphone output can match the impedance of your headphones. If the sound is strained going into the K66's, I think it will sound even more strained going into the 701's. You would probably do well to invest in a headphone amp that can match 701's impedance.

The K 701 needs a good amp, the better the amp the better it sounds.
I have 3 headphone amps: Meier Move(portable), Meier Cantate and DarkVoice 337.
The DV 337 is a world class tube amp. Dual mono, 2 tubes for each channel, 2 transformers, 2 volume pots and needs 2 power cords.
The K701 sounds great with all the above but gets better with each amp.
with a great source you will have a system that sounds as good as a 40,000
speaker based system.

The DV 337 can be bought for under 700.00 and NOS tubes are not expensive.
IMO you wont hear what the 701 is capable of W/O a great amp.

one other thing re K701

It sounds HORRIBLE out of the box. You will think it's worse than apple earbuds:-)

It needs 50 hours to become mediocre.
But after 200 hours of break in it starts to reveal it's potential.
It is a great headphone once broken in.

I agree about the transformation of the 701s. I found at 300-400 hours is when they seemed to sing. They were painful prior to that.

Quote:
I agree about the transformation of the 701s. I found at 300-400 hours is when they seemed to sing. They were painful prior to that.

I found them very bright and hard, but listened to them only when a friend loaned me his new pair with probably no more than 30-50 hours on them. I need to hear them again now.