Data from a microearthquake cluster in northern Switzerland and synthetic seismograms simulating the observed signals are used to compare two different techniques of obtaining information about earthquake source-time functions. Comparisons between the observed P-wave velocity pulse widths and the rise times of far-field displacement pulses obtained from empirical Green's function (EGF) deconvolutions show significant discrepancies. Whereas the observed velocity pulse widths of the larger events scale with seismic moment over a broad range, this scaling is practically lost in the deconvolutions. The reason is that velocity pulse widths are usually measured at high trace magnifications from the first break to the first zero crossing. At lower magnifications, these pulse widths are seen to include an emergent onset, which can be attributed to an initial phase of gradual rupture acceleration and whose duration scales with moment. Synthetic simulations, based on a source model of a circular crack with constant stress drop and rupture propagating outward from the center with a gradually increasing velocity, correctly reproduce these emergent onsets. Deconvolutions using the synthetic signals show that the slow initial phase is masked by the noise amplification and stabilizing measures inherent in the deconvolution. Therefore, despite the uncertainties in the necessary corrections for attenuation and scattering along the path, relative pulse width measurements are more reliable and provide better resolution for small earthquakes than rise-time measurements on far-field displacement pulses obtained from EGF deconvolutions by spectral division.