No Secrets was Simon’s commercial breakthrough. The album spent five weeks at number 1 on the Billboard charts and quickly went Gold, as did its leadoff single, “You’re So Vain“, which remained at number 1 on the Pop charts for three weeks, and at number 1 on the Adult Contemporary charts for two weeks. 25 years after its initial release, the album was officially certified Platinum on December 12, 1997.
Initial reviews for No Secrets were mixed mostly in an ironically positive vein. Robert Christgau, writing in Creem, rated the album only a B− and stated that “if a horse could sing in a monotone, the horse would sound like Carly Simon, only a horse wouldn’t rhyme “yacht,” “apricot,” and “gavotte.” Is that some kind of joke?” Stephen Holden in Rolling Stone was ironic in his praise concluding that “what finally makes No Secrets so refreshing is her singing, which conveys the finest spirit of patrician generosity.”
A more recent review from Allmusic‘s William Ruhlmann along with a high rating reflects a more positive regard for the album. Ruhlmann noted that “You’re So Vain” “set the album’s saucy tone, with its air of sexually frank autobiography and its reflections on the jet-set lifestyle.” He also stated that “now that she felt she had found true love, she was as willing to acknowledge her own mistakes and regrets as she was to point fingers.” But even he concluded on the note that “Perry paid particular attention to Simon’s vocals in a way that made her more engaging (or at least less grating) to listen to.”