Source and Qp parameters were estimated from the inversion of first arrival P waveform durations of about 300 microearthquakes recorded at a digital seismic network operating in southeastern Sicily. The average risetime and pulse width at each station do not show large differences, allowing us to exclude significant differential attenuation site effects. A first Qp estimate was obtained by applying the classical risetime method, under the assumption of a point-like source time function. In order to investigate the effect of directivity due to the finiteness of seismic sources, new nonlinear relationships, based on a circular crack model rupturing at a constant velocity, were numerically built. These relationships were used to formulate a nonlinear inverse method for retrieving source (radius, dip, and strike of the circular crack) and Qp parameters from the inversion of risetime and pulse width data. The application of the method produced a better fit of the observed data and a Qp value higher than that obtained by applying the risetime method. The discrepancy between the different Q estimates may be due to a trade-off among source dimension and Qp, as we inferred from a test on a subset of low-magnitude events (Ml ≤ 2.5). A good agreement with independent estimates of fault plane solutions, as inferred from P polarities and S polarizations, was found. The estimated stress drops are generally very low (0.1--10 bars). This suggests that the background seismic activity in southeastern Sicily is related to fault segments and/or weakened zones where great stress accumulations are hindered.