Little is known about Cui Cha's career before his brief stint as chancellor, as, atypical for a chancellor, he did not have a biography in either the Old Book of Tang or the New Book of Tang. It is, however, known that his family was from Lantian (藍田, in modern Xi'an, Shaanxi). As of 684, he was serving as an assistant censor (監察御史, Jiancha Yushi), when, in the midst of a rebellion by Li Jingye the Duke of Ying against Emperor Ruizong's powerful mother and regent Empress Dowager Wu (later known as Wu Zetian), the chancellor Pei Yan suggested that Empress Dowager Wu could quell Li's rebellion easily by returning imperial authority to Emperor Ruizong. When Cui heard of Pei's suggestion, he submitted a note to Empress Dowager Wu stating, "Pei Yan received great responsibilities to look after the emperor after the deceased emperor Dowager Wu's husband Emperor Gaozong) entrusted him with those great responsibilities. If he were not planning to commit treason, why would he want the Empress Dowager to give up her imperial powers?" In response, Empress Dowager Wu had Pei accused with and investigated for treason, and Pei was executed. Later that year, she made Cui, who was at that point an editor of the imperial archives (著作郎, Zhuzuo Lang), Zhengjian Daifu (正諫大夫), a senior advisor at the examination bureau of government (鸞臺, Luantai) and made him a chancellor de facto, with the designation Tong Fengge Luantai Pingzhangshi (同鳳閣鸞臺平章事), along with Shen Junliang. In spring 685, both he and Shen were removed from those posts. As of 689, Cui was serving as deputy minister of defense (夏官侍郎, Xiaguan Shilang), when, for reasons lost to history, Empress Dowager Wu had him assassinated.

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崔詧出自清河崔氏定著六房之一的南祖崔氏，崔詧任宰相之前的經歷幾乎沒有記載，《舊唐書》和《新唐書》一般有宰相的傳，卻都沒有他的傳。684年九月，崔詧時任監察御史，當時英國公李敬業反對睿宗的母親武則天臨朝稱制在揚州造反，宰相裴炎說太后將權力交給皇帝，叛亂自然平定。崔詧聽說後，上書太后：「裴炎受先帝顧命，大權在握，若無異心，為什麼要讓太后交權？」結果，武則天以裴炎勾結李敬業謀反之罪，將他處死。崔詧升任著作郎。十月，崔詧和時任右史（即起居舍人）的沈君諒被太后武則天任命為正諫大夫（即諫議大夫，隸屬于鸞臺-門下省），並同鳳閣鸞臺平章事，成為宰相。685年二月，沈君諒罷相。三月，崔詧罷相。689年九月，時任夏官侍郎的崔詧被武則天暗殺。