In the degree of its intelligence and forthrightness [No Secrets] is the equal of its predecessors….

The obvious highlight of No Secrets is the hit single, "You're So Vain," an affectionately high-spirited putdown of a male chauvinist glamour boy….

[Of the album's] other cuts, five take up the subject of time—lovers' time versus childhood time—playing variations on Carly's favorite theme. The implicit assumption behind these songs is the difficulty of being happy, especially when in love, without over-analyzing one's happiness so as to dissipate its intensity. The realization that emotion and rationalization are often irreconcilable is most painfully expressed in Carly's ballad, "We Have No Secrets."… With the exception of "You're So Vain," Carly's lyrics are stronger than her tunes.

Stephen Holden, in his review of "No Secrets," in Rolling Stone (by Straight Arrow Publishers, Inc. © 1973; all rights reserved; reprinted by permission), Issue 125, January 4, 1973, p. 64.