Efficient sequencing of dsDNA with extremely low level of errors

A method for sequencing DNA comprising:

• a) combining double-stranded DNA (dsDNA) fragments with:
• (i) Y-adapters each comprising a stem and (ii) hairpin adapters comprising an affinity-label, under conditions wherein at least some of the Y-adapters and at least some of the hairpin adapters ligate to at least some of the fragments forming a mixture of fragment-adapter complexes comprising:
• fragment inserts flanked by two Y-adapters (“YY complexes”),
• fragment inserts flanked by a Y-adapter on one end and a hairpin adapter on the other end (“hairpin complexes”), and
• fragment inserts flanked by two hairpin adapters (“dumbbell complexes”);
• and
• b) sequencing the fragment inserts of the hairpin complexes with sequencing primers selecting for the Y-adapters,
• wherein the Y-adapters comprise bases promoting mispairing at the stem of the Y-adapter sufficient to weaken zipper closing at the stem and promote annealing access by a sequencing primer.