Inversion of slant stacks for velocity-depth structures using only the intercept time tau(p) is suboptimal. We propose inverting slant stacks using their integrated power P(p) as an additional constraint. First-order discontinuities and changes in gradient of velocity-depth functions, v(z), cause losses of P(p) only for record sections of finite length. In practice then, the observed P(p) may be used to constrain v(z). One advantage of the proposed method is that both tau(p) and P(p) are found directly from the slant stack. Another advantage is that velocity structures are rapidly and accurately inferred. Finally, the method is not subject to biases, as are methods which employ first arrivals only.