  We present the discovery of 37 pulsars from $\sim$ 20 years old archival data
of the Parkes Multibeam Pulsar Survey using a new FFT-based search pipeline
optimised for discovering narrow-duty cycle pulsars. When developing our pulsar
search pipeline, we noticed that the signal-to-noise ratios of folded and
optimised pulsars often exceeded that achieved in the spectral domain by a
factor of two or greater, in particular for narrow duty cycle ones. Based on
simulations, we verified that this is a feature of search codes that sum
harmonics incoherently and found that many promising pulsar candidates are
revealed when hundreds of candidates per beam with even with modest spectral
signal-to-noise ratios of S/N$\sim$5--6 in higher-harmonic folds (up to 32
harmonics) are folded. Of these candidates, 37 were confirmed as new pulsars
and a further 37 would have been new discoveries if our search strategies had
been used at the time of their initial analysis. While 19 of these newly
discovered pulsars have also been independently discovered in more recent
pulsar surveys, 18 are exclusive to only the Parkes Multibeam Pulsar Survey
data. Some of the notable discoveries include: PSRs J1635$-$47 and J1739$-$31,
which show pronounced high-frequency emission; PSRs J1655$-$40 and J1843$-$08,
which belong to the nulling/intermittent class of pulsars; and PSR J1636$-$51,
which is an interesting binary system in a $\sim$0.75 d orbit and shows hints
of eclipsing behaviour -- unusual given the 340 ms rotation period of the
pulsar. Our results highlight the importance of reprocessing archival pulsar
surveys and using refined search techniques to increase the normal pulsar
population.
