Bube and Burridge (1983) have investigated direct inverse methods in the time domain for solving the acoustic equation in one space dimension for the impedance profile. Since every slowness in a proper slant stack is a rescaled plane wave component, the technique can legitimately be applied to each trace individually. We have developed a robust estimation procedure that combines the (overdetermined) set of solutions in the τ − p domain to invert not just the impedance profile but the density and wave velocity separately. We have successfully applied the method to synthetic seismogram data for which neither the density, the wave velocity, nor the impedance are monotone functions of depth. Satisfactory results have been obtained after convolution of the model seismograms with a variety of source wavelets and after addition of random noise of amplitude comparable in level to the rms signal. We note that our method and results are for an acoustic equation model which may be inappropriate for physical models which generate significant shear waves from interface conversions.