First, there is Carter's dreamy and poetic Boston Concerto, performed in 2008 by Oliver Knussen and the BBC SO. My old copy of this performance came from a very dynamically compressed FM broadcast. The present copy (sent to me by an online friend in U.K.) comes from a gloriously uncompressed BBC HD webstream (320 kbs AAC). On first hearing, it sounded like a completely different piece, not so much because of a much more refined sound quality, but because the dynamic range of the actual performance conveyed by the BBC HD stream is 9.0 db (!) wider than my old FM broadcast. (6.0 db already amounts to doubling the loudness difference between the loudest and the quietest parts.)
Then there is my first recording of Carter's charming 9-minute long Concertino for Bass Clarinet and Ensemble (2009). The performance was the US Premiere of the piece, given on June 18, 2009 by Virgil Blackwell and the Orchestra of the League of Composers at Columbia University's Miller Theater. The sound quality is on a mediocre side (it was extracted from HD video), primarily because of its rather distant perspective, which does not convey the interplay among instrumental sections with as much immediacy as Carter's music deserves.
Finally, there is a new copy, in improved sound, of Carter's irresistibly playful Two Controversies and A Conversation. The performance, given by Colin Currie and Eugen Huebner with the NY Philharmonic conducted by David Robertson, was originally offered by WQXR as a 128 kbs webcast. At a later time, the NY Phil itself offered this performance in 192 kbs bitrate, and with properly balanced channels (the WQXR webcast's right channel had about 3.0 db of excess loudness). The improvement may not be dramatic, but it is noticeable, and I thought it would be well to offer the new copy to Carter fans here. (New link added in comment #5.)