What does it mean when Imam at-Tirmidhi grades a hadith "hasan sahih"?

Students often find this puzzling, since a report would seem to be either hasan or sahih, not both at once. At-Tirmidhi himself, in al-'Ilal as-Saghir appended to his Jami', explains only what he means by "hasan" — a report in whose chain there is no one accused of lying, which is not shadh, and which is narrated through more than one route — and never spells out the composite term, so later scholars reconstructed his intent. The best-known resolution is Ibn Hajar's in Nuzhat an-Nazar: if the hadith has more than one chain, "hasan sahih" means it is hasan by one route and sahih by another; if it has only a single chain, the phrase indicates hesitation — hasan in the estimation of some critics and sahih in the estimation of others. Ibn as-Salah had already raised and answered the same objection in his Muqaddimah. In practice the label means at-Tirmidhi considered the report acceptable as evidence, though on the single-chain reading it is not automatically stronger than "sahih" said alone, and later critics examined each chain independently rather than accepting the label at face value.

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