A survey of the entire southern sky for millisecond and other low-luminosity pulsars using the Parkes radio telescope is described. Dual linear polarization receivers are used, each centred at 436 MHz, with a 256-channel filterbank system covering a bandwidth of 32 MHz. Observations are made with the telescope beam centred on an approximately hexagonal grid of 44299 positions, with an observation time of 157.3 s per pointing. The data are sampled at 300-μs intervals and recorded on magnetic tape. Off-line analyses are carried out on networked work-stations and involve de-dispersion, fast Fourier transform and harmonic summing. For any significant spectral features, time- and frequency-domain plots are formed. Selected candidate pulsars from this stage of analysis are reobserved at Parkes to check the reality of the detection. Away from the Galactic plane and for low-dispersion pulsars of pulse period greater than about 10 ms, the sensitivity of the survey is ≡3 mJy. Analysis of about 50 per cent of the planned survey has resulted in the detection of 201 pulsars, of which 55 are new discoveries. Eight of the new discoveries are millisecond pulsars; these have already been reported by Johnston et al., Bailes et al., and Lorimer et al. The observed distributions of the detected pulsars in period, dispersion measure, flux density and Galactic coordinates are described.