Let W(a) be Wiener-Hopf integral operator with piecewise continuous \(a\in L^{\infty}(R)\). The family of projections \(\{P_{\tau}\}_{\tau >0}\) is defined by \((P_{\tau}\psi)(x)=\psi (x)\) for \(0<x<\tau\) and 0 for \(x>\tau\). We will say that we are applying the reduction method to W(a) in \(L^ p(R_+)\) \((1<p<\infty)\) if for \(\tau \geq \tau_ 0\) the operators \(W_{\tau}(a)=P_{\tau}W(a)P_{\tau}| Im P_{\tau}\) are invertible and \(\sup \{\| W^{-1}_{\tau}(a)| Im P_{\tau}\|:\) \(\tau \geq \tau_ 0\}<\infty\) (we write \(W(a)\in \Pi_ P\{P_{\tau}\})\). Theorem 1. If W(a) is bounded in \(L^ p(R_+)\), \(W(a)\in \Pi_ p\{P_{\tau}\}\), then \(W(a)\in \Pi_ r\{P_{\tau}\}\) for all \(r\in [p,q]\), \(1/p+1/q=1\), and, consequently, W(a) is invertible in \(L^ r(R_+)\), \(r\in [p,q]\). Theorem 2. Let W(a) be bounded in \(L^ s(R_+)\) for all s in some neighborhood of p. If W(a) is invertible in \(L^ r(R_+)\) for all \(r\in [p,q]\), \(1/p+1/q=1\), then \(W(a)\in \Pi_ p\{P_{\tau}\}\).