A simple and practical method for source-waveform estimation from reflection seismic records is implemented by iterative identification of locally strongest reflections. Instead of conventional hypotheses about statistical properties of the whole records, the method is based on a general observation that stronger reflection peaks occur relatively sparsely and that smaller peaks adjacent to them are mutually incoherent. Tests with real well logs suggest that the subsurface often possesses such sparseness. Based on this property, the source waveform is obtained from seismic records by optimizing a combination of its practically important properties, such as the main-lobe width, side-lobe amplitudes, and phase character. Similarly, other types of optimization criteria can be used. The approach is stable with respect to noise and parameter variations and allows estimating the source waveforms without well-log control. By including inverse -filtering, time-variant amplitude scaling, and/or band-pass filtering, the approach allows correcting for reflection amplitude variations, nonstationarity due to seismic attenuation and dispersion, and also for coherent noise consisting in possible amplitude variations and phase shifts of the low- or high-frequency components of the records. By using the estimated source waveform, time-dependent waveforms and nonstationary wavelet matrices can be predicted at any reflection time. The method is illustrated by synthetic examples of logs with von Kármán distributions of velocity fluctuations and real well logs from an oil reservoir. In the synthetics, the spectral character and shape of the main lobe of the source waveform are reproduced well in all cases, and the phase character of the source is partly recovered when the subsurface reflectivity is dominated by reflections that are relatively sparse and strong compared to the adjacent reflectivity. In cases in which the phase of the source signal is unknown, the obtained waveforms are characterized by simple shapes with low-amplitude side lobes. Such waveforms are suitable for many applications from well ties and numerical modeling to deconvolution and -compensation.