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.
jpmcgrath
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 !