The performance of resonant piezoelectric vibration energy harvesters (RPVEHs) is strongly affected by the characteristics (shape, amplitude, spectrum, and so on) of the vibrations from which energy is harvested. In particular, the estimation of the power that can be harvested by a given RPVEH fed by a specific vibration source is of great importance for design purposes. A fast estimation of the extractable power allows an effective and proper sizing of the harvesting devices. This paper addresses this issue for non-sinusoidal vibration sources, filling the gap in the existing literature. To this end, an accurate and efficient analysis tool for RPVEH systems loaded by bridge rectifiers is provided. The estimation of the average extracted power as a function of the bridge rectifier dc output voltage is carried out for both weakly and non-weakly electromechanically coupled RPVEHs. A closed-form expression is provided for the case of amplitude-modulated vibrations, whereas an analytical-numerical expression is given in case of vibrations with a non-sinusoidal slowly varying envelope. Experimental tests, obtained by using a commercial RPVEH, validate the theoretical results.