Tube sound: Pre-amp vs. amp?

I'm just an audio neophyte, so bear with me on this question: If I want to achieve a "warmer", tube-like sound, do I have to upgrade BOTH the pre-amp and the amp to tubes? I currently have ss components (NAD) and would like to take the edge off the top, but keep the detail, especially in the mid-range.
You do not say what your source is! Assuming it's CD, might it be your CD player adding the HF edge? Regardless, a tube preamp will reduce the HF edge, but it will not remove the transistors from your SS amp. Transistors have their own sound as well. In short, yes, a tube preamp will warm your system. Be sure to try your choices in your own system to be sure you get the sound you seek.
Depending on how high end your CD Player is you may try an inexpensive tube buffer stage in between you player and amplifier. Musical Fidelity makes one for $200.00 (much less used) that does this trick but may slow the tempo somewhat per recent reviews and feedback. I assume that there must be other models that are also low cost. Maybe someone at this sight knows of them. The con is that you will need another pair of interconnects to hook it up.
Post removed 
You do not have to replace both your amp and preamp in order to introduce the sound of tubes. However, if you add a tube preamp, make sure it's output impedance is low enough to drive the input of your solid state amp. You may also need to replace your interconnect with something more revealing if you add a tube preamp. There are many good tube preamps around, my personal favorites are the Audible Illusions Modulus and the Quicksilver line stage. That said, I do not use a tube preamp because my most of my gear has to reside in a piece of furniture and tubes require ventilation. I had a Berning TF-10 that sounded great but was slowly cooking itself until I switched to a solid state preamp (Classe) with Quicksilver Mono Tube amplifiers. This gives me a balance of solid state detail and control and tube warmth and bloom. I have also had to experiment with different cables in order to get the overall sound to gel properly. Before changing your current electronics you may want to experiment with some cables (try Harmonic Technology) and see if your can remove some of the edge you hear.
Joe is right about Harmonic Technology. I purchased their Truthlink interconnect ($125.00 used) to take the edge off of poor recordings and it does, though I prefer my Homegrown silver IC's for everything else. Listing the rest of your equipment would help as their may be an obvious cause that someone can identify. Also budget is a must for credible recommendations.
I've tried tube pre/solid state amp, and solid state pre/ tube amp. I found I got a lot more pleasing 'tube sound' with the tube amp. The preamp didn't seem to add enough tube euphony (audible illusions 3a) to be worth the loss in detail (to my adcom 750). Results and taste may vary !
It is always best to make sure your source components are the best that fits your needs/budget (cd player, tuner and turntable/tape deck). The rest of your system, wires-pre and power amps...and speakers will only have what is feed them by the source components to work with. That said, if you are happy with your front end (source) components, I would suggest trying tubes in the pre-amp and seeing if you like that first.
As you can readily tell from the responses, many amps have easily identifiable characteristics usually refered to as a "sound". If your priorities include an effort to approach a natural quality of sound, then I suggest that you listen extensively to acoustic instruments and voices in performance and then use that perceived sound quality as your standard. If your priority is to just have your system sound pleasing to YOUR ears with no desire to come close to the original sonic characteristics, then simply purchase what sounds good to you. Tubes are still well-liked by many I think because, generally speaking, they roll-off the top and fatten the bottom. This may make certain stridently rendered digital recordings more attractive and enjoyable to listen to. It should be pointed out that ss gear can be designed to closely replicate the qualities of tube equipment. The converse is less easy to achieve and to a large extent, not do-able. In any case, given the variables of equipment interactive relationships, individual levels of experience and sensitivities, and particularly, TASTE, there is little assurance that anyone's opinion will be reliable for you. I can assure you that if you prefer tube amplification, you should be prepared for changes of sonic attributes with every tube change. It's interesting that "audiophiles" will often spend thousands to make subtle changes in system characteristics. I.e., tonal modifications (sometimes, in effect, very expensive tone controls), Yet, the often shunned simple tone control will sometimes offer a sufficient solution. This leads me to a heretical suggestion; in your search you might also consider trying a pre-amp which offers you the option of some tone controls. You might be surprised at how effective one can be. A very nice, moderately priced one has been made by Musical Fidelity in the past. Of course, there are other options which don't involve hardware changes. I'm sure that there would also be many suggestions for that too:
john_1 sez: "... Results and taste may vary ! " i gotta agree w/that! ;~) in *my* case, a tubed preamp made a *big* difference - big increase in soundstage depth w/*no* loss of detail (to my linn kairn w/slimline version of their brilliant switch-mode p/s). of course, my electrocompaniet amps have been *accused* of being wery toob-like... it costs less money to get a tube preamp that doesn't sacrifice what solid-state offers, than to do the same w/a tube amp, imho... doug
I currently use a BAT VK3i tube preamp to drive my Marsh A400S 200 wpc solid state amp. Although the VK3i is a well regarded piece of equipment in my mind it adds unnecessary distortion to the signal. To me the best pre amp is NO PREAMP. Also I am not enthusuastic about tubes which as mentioned above roll off the top end and fatten the bass. I therefore plan to get rid of my preamp as soon as I get the chance, and replace it with the simplest high quality solid state unit I can find. Actually, the volume control is the most important part of the preamp ! In the 21st century it does not make sense to use tubes to equalize your music. It is much better to use on the new digital correction systems from Sigtech or Tact.