Is there a cd player that sounds close to an LP?


I am not sure what to do at this point. My system sounds great when I play my turntable.
I have a Marantz CD-67SE CD player, not high end by any means, but not a bad lower end player, so I thought. When I play CDs the brightness actually hurts my ears when I turn the volume up a bit.
I have been considering buy new cables for the speakers, maybe control this brightness, MIT T2's. Then was thinking, hate to ruin the sound I currently have from my platter. The highs and bass are perfect.
I have been considering buying an older tube CD player, in search of a warmer sound. I am thinking an Anthem CD1, a Conrad Johnson DV2B, maybe a Sonic Frontiers SFCD1. Not really sure what to buy.
Am I on the right track? I hate to change the sound of my system for CD's, and take away from the sound of my lp's.
Is there really a CD player out there that sounds even close to a LP? Maybe one that I might be able to pick up used for about a grand?
Any suggestions here, sure appreciate it!

Thank you.
johnymac
A few years ago, after I moved back to my mom's house for the summer, I had the loft for my stereo system. The acoustics in the loft was pretty bad. I had to move the system around the den before even the LPs sounded adequate. But, the CD always sounded dry and bright. I then upgraded the Marantz 63SE to CAL Delta/Sigma. Things improved, but the LP still sounded much better.

At the suggestion of DeKay, I removed all the cables and gave all the connections a good polish. I separated all the powercables from signal cables. And, I separated the digital stuff from the amp stuff. Afterwards, even the CD became listenable again.

Dekay is just the man!
No, but I can point you in the direction of a TT whose sound is closer to the positive attributes of a CD: modded Technics 1200 with tonearm fluid damper. Read Zaikesman's review in the accessories section.

It is my goal to keep my CD and vinyl playback close to each other and balanced, performacewise. I had a serious conversation with Dusty Vawter about this subject prior to buying his DAC.

To answer your question directly, you need to attack noise control, damping and isolation in your digital rig. This will assure the smoothest, jitter and artifact free playback possible.
A couple of recommendations: a tube-equipped CD-player such as the Shanling TCD-200, or upgrading your existing player with a DAC such as Musical Fidelity's or Chord's DAC64. I went for the Chord, and like the sound very much. As urged above: Go and hear for yourself. I think the rigid affirmations "CDs never can sound as good as LP" are no longer true. There's by now a lot of excellently produced, or remastered CDs (not SACD, DVD-Audio) that, given goog CD-players, sound excellent, sometimes better than the old LPs. Good examples are a lot of remastered CDs from the EMI "Great Recordings of the Century"-series. Then, there is the XRCD-series from JVC. In Germany, even high-end-die-hard-vinyl-pope Attila Csampai was forced to admit that they sounded better than the original LPs on his state-of-the-art turntable system. I did a vinyl-CD-comparison with a vinyl-fan, and even fooled him when playing from CD.
I recently acquired a Mark Levinson 390S which I play through an Audio Research Ref 2 Mk II preamp, ARC VTM200 monoblocks, and Acoustat 2+2 full range electrostatic speakers. These speakers will show ANY digital harshness at all if it's present, and THERE SIMPLY IS NONE with this CD player. I can listen to CD's for hours, and it even lulls me to sleep sometimes. I also listen to a lot of vinyl, especially new records I buy off of ebay that have never been played. The best LP's have a magic and "rightness" that the CD's do not, but this is the first CD player I've ever heard that I consider a legitimate audiophile product.