Running CD-Player Directly from Amp

I'm curious about the impressions of audiophiles regarding the use of a CD-Player's variable output for volume control while running it directly from a power amp. It seems like an ideal solution for a digital-only music listener, but doesn't the sound quality end up depending on the quality of the CDP's volume control?

Short of, say, a Wadia 850, are there any other CDP's (<$2,000) that give good results when used without a pre-amp?