We present the results of a 430-MHz survey for pulsars conducted during the upgrade to the 305-m Arecibo radio telescope. Our survey covered a total of 1147 deg2 of sky using a drift-scan technique. We detected 33 pulsars, 10 of which were not known prior to the survey observations. The highlight of the new discoveries is PSR J0407+1607, which has a spin period of 25.7 ms, a characteristic age of 1.5 Gyr and is in a 1.8-yr orbit about a low-mass (>0.2 M⊙) companion. The long orbital period and small eccentricity (e = 0.0009) make the binary system an important new addition to the ensemble of binary pulsars suitable to test for violations of the strong equivalence principle. We also report on our initially unsuccessful attempts to detect optically the companion to J0407+1607, which imply that its absolute visual magnitude is >12.1. If, as expected on evolutionary grounds, the companion is an He white dwarf, our non-detection implies a cooling age of least 1 Gyr.