We studied the fast timing behaviour of the atoll source 4U 1705–44 using the entire EXOSAT dataset, four observations covering a total of 230 000 seconds of 1–20 keV spectral and timing data. In one of the observations, 4U 1705–44 was in a low intensity “island” state and had an unusually hard spectrum. The fast timing analysis of this hard island state shows a power spectrum very similar to that of black hole candidates in the ‘low state’, with a flat-topped band-limited noise component that gradually steepens towards higher frequency. We perform for the first time a quantitative comparison of the timing behaviour of an atoll source in the hard island state (4U 1705–44) with that of a black hole candidate in the low state (Cygnus X-1). We also compare the power spectrum of 4U 1705–44 in the hard island state with those of the atoll source 4U 1608–52 in a similar state as reported by Yoshida et al. (1993). Our results confirm that there are similarities between the fast timing behaviour of the hard island states of these atoll sources and the low state of black hole candidates, yet we also find significant differences in power spectral parameters; the power spectra of the neutron star systems have a lower rms amplitude and are less steep. We find a trend among the neutron star power spectral properties, in the sense that the lower the centroid frequency of the fitted Lorentzian is, the higher its fractional rms amplitude, and the steeper the continuum underneath it. In our analysis we subtracted the instrumental band-limited noise component intrinsic to the EXOSAT ME that we found in our previous work on Cyg X-3, which contaminates the power spectra up to 100 Hz. We found that this component significantly affects the observed power spectra. We propose a new method to fit the power spectra of Cyg X-1 and other black hole candidates in the low state, that provides a significantly better fit than previous models.