“The undying creep of "Thanks, Anyway" weaves a misleadingly frail air about itself and begins the album in a deceptive light, but that deception is almost certainly deliberate. By the time you've reached the end of the road, you realize you're right back at the beginning. If Curves of Sirens were a film, it would be the kind of Usual Suspects "gotcha" that I've never before noticed in an album—a sonic set-up. For that twist alone, I suggest giving it a spin...”
— Justin Kownacki, Splendid, May 27, 2004

“This is an album all about build. Build up and tear down. Emotional ride to the climax build. Building a wall of harmonic guitar lines. Remarkably, the band pulls this off with their guitar builds... It is, in fact, this gift, this beauty of music that bands strive for. It is, in many ways, the musical ideal...”
— Jonathan Novak, Left Off the Dial, June 28, 2004

“..orchestrations cascade with an operatic beauty and remain calm and collected, while maintaining a sense of sedated mournfulness...”
— Dave Kargol, Skratch #99, May 2004