During the last decade, awareness has grown that the glottis does not necessarily close completely during normal phonation. To what extent a glottal leak affects the glottal flow waveform, however, is still poorly understood. A speech production model is implemented that is capable of simulating source/tract interaction using a time-varying glottal impedance analogous to that in the two-mass glottal model of Ishizaka and Flanagan. The original formulas are extended to incorporate two different types of glottal leakage: (1) a leak that is in open connection with the membranous part of the glottis, and (2) a leak formed by a separate duct (e.g., in the posterior commissure). However, instead of letting the glottal geometry be defined by a self-oscillating mechanical model of the vocal folds, the glottal inlet and outlet areas are prescribed by the authors. In the present simulations it is found that for a moderate leak area the flow through a type 2 leak and the flow through the membranous part may be in opposite directions during the interval that the folds close, thus enhancing the excitation of the vocal tract. Another interesting consequence of this result is that a physical explanation might be given for some of the waveform details sometimes observed in inverse filtered speech that are often considered as artifacts of the inverse filtering method.